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Methane clathrate hydrates, particularly those with an sI structure, are significant due to their potential as energy resources and their impact on gas pipelines. In this study, a two-dimensional (2D) lattice-gas model is employed to investigate the main thermodynamic properties of methane clathrate hydrates. The proposed framework is validated through comparison with experimental data and more advanced three-dimensional (3D) simulations. Adsorption isotherms, dissociation enthalpy and phase stability of the sI structure are evaluated using Monte Carlo (MC) simulations in the grand canonical ensemble. The 2D adsorption isotherms closely align with both experimental data and 3D simulations, demonstrating the 2D model's ability to precisely represent both rigid and flexible sI structures. The dissociation enthalpy calculated using our approach (76.4 kJ/mol) excellently matches the experimental value (78 kJ/mol), confirming the model's accuracy. Furthermore, the phase diagram obtained from the Clausius-Clapeyron equation shows very good agreement with experimental data between 260 and 290 K, though deviations are observed above 290 K. These findings underscore the effectiveness and robustness of the 2D model in studying methane clathrate hydrates and suggest its potential applicability for investigating other guest species and hydrate structures.

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard (inverse) percolation, the lattice is initially empty(occupied) and linear $k$-mers ($k$ linear consecutive sites) are randomly and sequentially deposited on(removed from) the lattice, considering an isotropic and nematic scheme. The study is conducted by following the behavior of four critical concentrations with the size $k$, determined for a wide range of $k$ : $(i)$[$(ii)$] standard isotropic[nematic] percolation threshold $\theta_{c,k}$[$\vartheta_{c,k}$], and $(iii)$[$(iv)$] inverse isotropic[nematic] percolation threshold $\theta^i_{c,k}$[$\vartheta^i_{c,k}$]. The obtained results indicate that: $(1)$ $\theta_{c,k}$[$\theta^i_{c,k}$] exhibits a non-monotonous dependence with $k$. It decreases[increases], goes through a minimum[maximum] around $k = 11$, then increases and asymptotically converges towards a definite value for large $k$ $\theta_{c,k \rightarrow \infty}=0.500(2)$[$\theta^i_{c,k \rightarrow \infty}=0.500(1)$]; $(2)$ $\vartheta_{c,k}$[$\vartheta^i_{c,k}$] rapidly increases[decreases] and asymptotically converges towards a definite value for infinitely long $k$-mers $\vartheta_{c,k \rightarrow \infty}=0.5334(6)$[$\vartheta^i_{c,k \rightarrow \infty}=0.4666(6)$]; $(3)$ for both models, the curves of standard and inverse percolation thresholds are symmetric with respect to $\theta = 0.5$. Thus, a complementary property is found $\theta_{c,k} + \theta^i_{c,k} = 1$ (and $\vartheta_{c,k} + \vartheta^i_{c,k} = 1$), which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems; and $(4)$ in all cases, the model presents percolation transition for the whole range of $k$.

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of $k \times k$ square tiles ($k^{2}$-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then, the system is diluted by removing $k^{2}$-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, $p_{c,k}$, for which the connectivity disappears. This particular value of the concentration is called \textit{inverse percolation threshold}, and determines a well-defined geometrical phase transition in the system. The results obtained for $p_{c,k}$ show that the inverse percolation threshold is a decreasing function of $k$ in the range $1 \leq k \leq 4$. For $k \geq 5$, all jammed configurations are percolating states, and consequently, there is no non-percolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent $\nu_j$ was measured, being $\nu_j = 1$ regardless of the size $k$ considered. In addition, the accurate determination of the critical exponents $\nu$, $\beta$ and $\gamma$ reveals that the percolation phase transition involved in the system, which occurs for $k$ varying between 1 and 4, has the same universality class as the standard percolation problem.

Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal and random lattices is studied. The adsorption process is modeled by using random sequential adsorption (RSA) algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension $d$ between 1 and 2, and on Erdos-Renyi random graphs. The number of sites is $M=L^d$ for Euclidean and fractal lattices, where $L$ is a characteristic length of the system. In the case of random graphs it does not exist such characteristic length, and the substrate can be characterized by a fixed set of $M$ vertices (sites) and an average connectivity (or degree) $g$. The paper concentrates on measuring (1) the probability $W_{L(M)}(\theta)$ that a lattice composed of $L^d(M)$ elements reaches a coverage $\theta$, and (2) the exponent $\nu_j$ characterizing the so-called "jamming transition". The results obtained for Euclidean, fractal and random lattices indicate that the main quantities derived from the jamming probability $W_{L(M)}(\theta)$ behave asymptotically as $M^{1/2}$. In the case of Euclidean and fractal lattices, where $L$ and $d$ can be defined, the asymptotic behavior can be written as $M^{1/2} = L^{d/2}=L^{1/\nu_j}$, and $\nu_j=2/d$.

The percolation behavior of aligned rigid rods of length $k$ ($k$-mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The $k$-mers, containing $k$ identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability $R_{L,k}(p)$ that a lattice composed of $L \times L$ sites percolates at a concentration $p$ of sites occupied by particles of size $k$. The results, obtained for $k$ ranging from 2 to 80, showed that the percolation threshold $p_c(k)$ exhibits a increasing function when it is plotted as a function of the $k$-mer size. The dependence of $p_c(k)$ was determined, being $p_c(k)=A+B/(C+\sqrt{k})$, where $A = p_c(k \rightarrow \infty)= 0.582(9)$ is the value of the percolation threshold by infinitely long $k$-mers, $B =-0.47(0.21)$ and $C = 5.79(2.18)$. This behavior is completely different to that observed for square lattices, where the percolation threshold decreases with $k$. In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the nematic axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of $k$ considered.

A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics and Wu's distribution are recovered in the limit of non-correlated states of the multiple exclusion statistics. In addition, an exclusion spectrum function $\mathcal{G}(n)$ is introduced to account for the dependence of the state exclusion on the occupation-number $n$. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size $k$ ($k$-mers) where multiple exclusion occurs. Remarkable agreement is found with Grand-Canonical Monte Carlo simulations from $k$=2 to 10 where multiple exclusion dominates as $k$ increases., Comment: 5 pages, 3 figures. Final version to be published in Physical Review Letters

Jamming and percolation of three-dimensional (3D) $k \times k \times k $ cubic objects ($k^3$-mers) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The $k^3$-mers were irreversibly deposited into the lattice. Jamming coverage $\theta_{j,k}$ was determined for a wide range of $k$ ($2 \leq k \leq 40$). $\theta_{j,k}$ exhibits a decreasing behavior with increasing $k$, being $\theta_{j,k=\infty}=0.4204(9)$ the limit value for large $k^3$-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent $\nu_j$ was measured, being $\nu_j \approx 3/2$. On the other hand, the obtained results for the percolation threshold $\theta_{p,k}$ showed that $\theta_{p,k}$ is an increasing function of $k$ in the range $2 \leq k \leq 16$. For $k \geq 17$, all jammed configurations are non-percolating states, and consequently, the percolation phase transition disappears. The interplay between the percolation and the jamming effects is responsible for the existence of a maximum value of $k$ (in this case, $k = 16$) from which the percolation phase transition no longer occurs. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size $k$ considered., Comment: 26 pages, 9 figures. arXiv admin note: text overlap with arXiv:1905.11438

Jamming and percolation of square objects of size $k \times k$ ($k^2$-mers) isotropically deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The $k^2$-mers were irreversibly deposited into the lattice. Jamming coverage $\theta_{j,k}$ was determined for a wide range of $k$ ($2 \leq k \leq 200$). $\theta_{j,k}$ exhibits a decreasing behavior with increasing $k$, being $\theta_{j,k\rightarrow\infty}=0.4285(6)$ the limit value for large $k^2$-mer sizes. On the other hand, the obtained results shows that percolation threshold, $\theta_{c,k}$, has a strong dependence on $k$. It is a decreasing function in the range $2 \leq k \leq 18$ with a minimum around $k=18$ and, for $k \geq 18$, it increases smoothly towards a saturation value. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size $k$ considered., Comment: 17 pages, 8 figures. arXiv admin note: text overlap with arXiv:1905.11440

The critical point of the condensation transition for linear molecules adsorbed on square lattices, was studied by using an adaptation of the Histogram Reweighting technique. The results were obtained by means of grand canonical Monte Carlo simulations within the lattice gas model, along with finite size scaling using the fourth order Binder cumulant. The Method was tested in a system of interacting monomers in which the critical point can be determined exactly. The application of this method to the determination of the critical point in dimer systems with attractive interactions, gave better results than the previous reported studies to the best knowledge of the authors. In addition, the adsorption isotherms at different temperatures, as well as the phase diagrams for monomer and dimer systems were obtained, achieving significant improvements in the phase diagram for dimers.

Monte Carlo simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of linear $k$-mers (also known as rods or needles) on the two-dimensional triangular lattice, considering an isotropic RSA process on a lattice of linear dimension $L$ and periodic boundary conditions. Extensive numerical work has been done to extend previous studies to larger system sizes and longer $k$-mers, which enables the confirmation of a nonmonotonic size dependence of the percolation threshold and the estimation of a maximum value of $k$ from which percolation would no longer occurs. Finally, a complete analysis of critical exponents and universality have been done, showing that the percolation phase transition involved in the system is not affected, having the same universality class of the ordinary random percolation., Comment: 6 figures

The statistical thermodynamics of binary mixtures of polyatomic species was developed on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear $k$-mers and $l$-mers (species occupying $k$ sites and $l$ sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. The process is analyzed through the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorption of interacting polyatomic mixtures., Comment: 27 pages, 8 figures

Random sequential adsorption of straight rigid rods of length $k$ ($k$-mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for \textit{k} ranging from 2 to 64, revealed that (i) in the case of dimers ($k=2$), the jamming coverage is $\theta_j=0.918388(16)$. Our estimate of $\theta_j$ differs significantly from the previously reported value of $\theta_j=0.799(2)$ [Y. Y. Tarasevich and V. A. Cherkasova, Eur. Phys. J. B \textbf{60}, 97 (2007)]; (ii) $\theta_j$ exhibits a decreasing function when it is plotted in terms of the $k$-mer size, being $\theta_j (\infty)= 0.4045(19)$ the value of the limit coverage for large $k$'s; and (iii) the ratio between percolation threshold and jamming coverage shows a non-universal behavior, monotonically decreasing with increasing $k$., Comment: 6 pages, 4 figures

The statistical thermodynamics of polyatomic species mixtures adsorbed on two-dimensional substrates was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the coverage and temperature dependence of the Helmholtz free energy and chemical potential are given. The formalism leads to the exact statistical thermodynamics of binary mixtures adsorbed in one dimension, provides a close approximation for two-dimensional systems accounting multisite occupancy and allows to discuss the dimensionality and lattice structure effects on the known phenomenon of adsorption preference reversal., Comment: 13 pages, 4 figures

The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SAARs) model, the surface is represented by a twodimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a one-dimensional behavior in this regime. Finally, the universality class of the SAARs model, which has been subject of controversy, has been revisited., Comment: paper (13 pages, 8 figures); supplementary information (17 pages)

Monte Carlo (MC) simulations have been carried out to study the adsorption on square and triangular lattices of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with a discrete number of allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The process has been monitored by following the behavior of the adsorption isotherms for different values of lateral interaction energy/temperature. The numerical data were compared with mean-field analytical predictions and exact functions for noninteracting and 1D systems. The obtained results revealed the existence of three adsorption regimes in temperature. (1) At high temperatures, above the critical one characterizing the IN transition at full coverage Tc(\theta=1), the particles are distributed at random on the surface and the adlayer behaves as a noninteracting 2D system. (2) At very low temperatures, the asymmetric monomers adsorb forming chains over almost the entire range of coverage, and the adsorption process behaves as a 1D problem. (3) In the intermediate regime, the system exhibits a mixed regime and the filling of the lattice proceeds according to two different processes. In the first stage, the monomers adsorb isotropically on the lattice until the IN transition occurs in the system and, from this point, particles adsorb forming chains so that the adlayer behaves as a 1D fluid. The two adsorption processes are present in the adsorption isotherms, and a marked singularity can be observed that separates both regimes. Thus, the adsorption isotherms appear as sensitive quantities with respect to the IN phase transition, allowing us (i) to reproduce the phase diagram of the system for square lattices and (ii) to obtain an accurate determination of the phase diagram for triangular lattices., Comment: Langmuir, 2012

The statistical thermodynamics of straight rigid rods of length $k$ on triangular lattices was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives were written in terms of the order parameter $\delta$, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with $\delta$ as a parameter, the main adsorption properties were calculated. Comparisons with Monte Carlo simulations and experimental data were performed in order to evaluate the reaches and limitations of the theoretical model., Comment: 21 Pages; 4 Figures

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length $k$ ($k$-mers) on two-dimensional square lattices. The $k$-mers, containing $k$ identical units (each one occupying a lattice site), were adsorbed at equilibrium on the lattice. The process was monitored by following the probability $R_{L,k}(\theta)$ that a lattice composed of $L \times L$ sites percolates at a concentration $\theta$ of sites occupied by particles of size $k$. A nonmonotonic size dependence was observed for the percolation threshold, which decreases for small particles sizes, goes through a minimum, and finally asymptotically converges towards a definite value for large segments. This striking behavior has been interpreted as a consequence of the isotropic-nematic phase transition occurring in the system for large values of $k$. Finally, the universality class of the model was found to be the same as for the random percolation model., Comment: 21 pages, 4 figures

The critical behavior of self-assembled rigid rods on a square lattice was recently reinvestigated by Almarza et al. [Phys. Rev. E 82, 061117 (2010)]. Based on the Binder cumulants and the value of the critical exponent of the correlation length, the authors found that the isotropic-nematic phase transition occurring in the system is in the two-dimensional Ising universality class. This conclusion contrasts with that of a previous study [L\'opez et al., Phys. Rev. E 80, 040105 (R) (2009)] which indicates that the transition at intermediate density belongs to the q = 1 Potts universality class. Almarza et al. attributed the discrepancy to the use of the density as the control parameter by L\'opez et al. The present work shows that this suggestion is not sufficient, and that the discrepancy arises solely from the use of different statistical ensembles. Finally, the necessity of making corrections to the scaling functions in the canonical ensemble is discussed., Comment: 3 pages, 2 figures, accepted for publication in Physical Review E

The monolayer adsorption process of interacting binary mixtures of species $A$ and $B$ on square lattices is studied through grand canonical Monte Carlo simulation in the framework of the lattice-gas model. Four different energies have been considered in the adsorption process: 1) $\epsilon_0$, interaction energy between a particle (type $A$ or $B$) and a lattice site; 2) $w_{AA}$, interaction energy between two nearest-neighbor $A$ particles; 3) $w_{BB}$, interaction energy between two nearest-neighbor $B$ particles; 4) $w_{AB}=w_{BA}$, interaction energy between two nearest-neighbors being one of type $A$ and the other of type $B$. The adsorption process has been monitored through total and partial isotherms and differential heats of adsorption corresponding to both species of the mixture. Our main interest is in the repulsive lateral interactions, where a variety of structural orderings arise in the adlayer, depending on the interaction parameters ($w_{AA}$, $w_{BB}$ and $w_{AB}$). At the end of this work, we determine the phase diagram characterizing the phase transitions occurring in the system. A nontrivial interdependence between the partial surface coverage of both species is observed.

We study the two-dimensional Edwards-Anderson spin-glass model using a parallel tempering Monte Carlo algorithm. The ground-state energy and entropy are calculated for different bond distributions. In particular, the entropy is obtained by using a thermodynamic integration technique and an appropriate reference state, which is determined with the method of high-temperature expansion. This strategy provide accurate values of this quantity for finite-size lattices. By extrapolating to the thermodynamic limit, the ground-state energy and entropy of the different versions of the spin-glass model are determined., Comment: 18 pages, 5 figures

Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of self-assembled rigid rods on triangular and honeycomb lattices at intermediate density has been studied. The system is composed of monomers with two attractive (sticky) poles that, by decreasing temperature or increasing density, polymerize reversibly into chains with three allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the IN transition belongs to the q=1 Potts universality class., Comment: 6 pages, 5 figures

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results., Comment: 12 pages, 10 figures, supplementary information

In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models., Comment: 16 pages and 21 figures

Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of attractive rigid rods of length k (k-mers) on square lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel k-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density \theta_c, which increases linearly with the magnitude of the lateral interactions., Comment: 7 pages, 6 figures

Monte Carlo simulations have been carried out for a system of monomers on square lattices that, by decreasing temperature or increasing density, polymerize reversibly into chains with two allowed directions and, at the same time, undergo a continuous isotropic-nematic (I-N) transition. The results show that the self-assembly process affects the nature of the transition. Thus, the determination of the critical exponents indicates that the universality class of the I-N transition changes from two-dimensional Ising-type for monodisperse rods without self-assembly to q=1 Potts-type for self-assembled rods., Comment: 4 pages, 5 figures. Final version accepted for publication in PRE (Rapid Communications)

A simple statistical mechanical approach for studying multilayer adsorption of interacting polyatomic adsorbates (k-mers) has been presented. The new theoretical framework has been developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams (BWA) and quasi-chemical (QCA) approximations. The derivation of the equilibrium equations allows the extension of the well-known Brunauer-Emmet-Teller (BET) isotherm to more complex systems. The formalism reproduces the classical theory for monomers, leads to the exact statistical thermodynamics of interacting k-mers adsorbed in one dimension, and provides a close approximation for two-dimensional systems accounting multisite occupancy and lateral interactions in the first layer. Comparisons between analytical data and Monte Carlo simulations were performed in order to test the validity of the theoretical model. The study showed that: (i) the resulting thermodynamic description obtained from QCA is significantly better than that obtained from BWA and still mathematically handable; (ii) for non-interacting k-mers, the BET equation leads to an underestimate of the true monolayer volume; (iii) attractive lateral interactions compensate the effect of the multisite occupancy and the monolayer volume predicted by BET equation agrees very well with the corresponding true value; and (iv) repulsive couplings between the admolecules hamper the formation of the monolayer and the BET results are not good (even worse than those obtained in the non-interacting case)., Comment: 38 pages, 12 figures

In this work we study the multilayer adsorption of polyatomic species on homogeneous and heterogeneous bivariate surfaces. A new approximate analytic isotherm is obtained and validated by comparing with Monte Carlo simulation. Then, we use the well-known Brunauer-Emmet-Teller's (BET) approach to analyze these isotherms and to estimate the monolayer volume, $v_\mathrm{m}$. The results show that the value of the $v_\mathrm{m}$ obtained in this way depends strongly on adsorbate size and surface topography. In all cases, we find that the use of the BET equation leads to an underestimate of the true monolayer capacity., Comment: 21 pages, 13 figures

In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold $\theta_c$ of the adlayer, which presents an interesting dependence with $w/k_BT$ (being $w$, $k_B$ and $T$, the lateral interaction energy, the Boltzmann's constant and temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a non-percolating region is determined., Comment: 25 pages, 12 figures, figures missing in previous version

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems., Comment: 30 pages, 17 figures. A new section added. Accepted for publication in Physica A

In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattice are found. A phase diagram separating a percolating from a non-percolating region is determined. The main features of the phase diagram are discussed in terms of simple considerations related to the interactions present in the problem. The influence of the phase transitions occurring in the system is reflected by the phase diagram. In addition, a scaling treatment maintaining constant the surface coverage and varying the temperature of the system is performed. In all the considered cases, the universality class of the model is found to be the same as for the random percolation model., Comment: 19 pages, 8 figures

The critical behavior of long straight rigid rods of length $k$ ($k$-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel $k$-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density $\theta_c$. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of $\theta_c$ on $k$, being $\theta_c(k) \propto k^{-1}$. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of $k$ ($k_{min}=7$), which allows the formation of a nematic phase on a triangular lattice., Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physics

The deposition of a metal on a foreign substrate is studied by means of grand canonical Monte Carlo simulations and a lattice-gas model with pair potential interactions between nearest neighbors. The influence of temperature and surface defects on adsorption isotherms and differential heat of adsorption is considered. The general trends can be explained in terms of the relative interactions between adsorbate atoms and substrate atoms. The systems Ag/Au(100), Ag/Pt(100), Au/Ag(100) and Pt/Ag(100) are analyzed as examples., Comment: 26 pages, 9 figures

The isotropic-nematic (I-N) phase transition in a system of long straight rigid rods of length k on square lattices is studied by combining Monte Carlo simulations and theoretical analysis. The process is analyzed by comparing the configurational entropy of the system with the corresponding to a fully aligned system, whose calculation reduces to the 1D case. The results obtained (1) allow to estimate the minimum value of k which leads to the formation of a nematic phase and provide an interesting interpretation of this critical value; (2) provide numerical evidence on the existence of a second phase transition (from a nematic to a non-nematic state) occurring at density close to 1 and (3) allow to test the predictions of the main theoretical models developed to treat the polymers adsorption problem., Comment: 14 pages, 6 figures. Accepted for publication in JSTAT

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on two-dimensional lattices. The nematic phase, characterized by a big domain of parallel $k$-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the transition belongs to the 2D Ising universality class for square lattices and the three-state Potts universality class for triangular lattices., Comment: 7 pages, 8 figures, uses epl2.cls, to appear in Europhysics Letters

Monte Carlo simulations and finite-size scaling theory have been used to study the critical behavior of repulsive dimers on square lattices at 2/3 monolayer coverage. A "zig-zag" (ZZ) ordered phase, characterized by domains of parallel ZZ strips oriented at $\pm 45^o$ from the lattice symmetry axes, was found. This ordered phase is separated from the disordered state by a order-disorder phase transition occurring at a finite critical temperature. Based on the strong axial anisotropy of the ZZ phase, an orientational order parameter has been introduced. All the critical quantities have been obtained. The set of critical exponents suggests that the system belongs to a new universality class., Comment: 9 pages, 9 figures. Accepted for publication in PRB

We study the phase stability of the Edwards-Anderson spin-glass model by analyzing the domain-wall energy. For the bimodal distribution of bonds, a topological analysis of the ground state allows us to separate the system into two regions: the backbone and its environment. We find that the distributions of domain-wall energies are very different in these two regions for the three dimensional (3D) case. Although the backbone turns out to have a very high phase stability, the combined effect of these excitations and correlations produces the low global stability displayed by the system as a whole. On the other hand, in two dimensions (2D) we find that the surface of the excitations avoids the backbone. Our results confirm that a narrow connection exists between the phase stability of the system and the internal structure of the ground-state. In addition, for both 3D and 2D we are able to obtain the fractal dimension of the domain wall by direct means., Comment: 4 pages, 3 figures. Accepted for publication in Rapid Communications of Phys. Rev. B

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas of interacting monomers adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure. The model mimics a nanoporous environment, where each nanotube or unit cell is represented by a one-dimensional array. Two kinds of lateral interaction energies have been considered: $1)$ $w_L$, interaction energy between nearest-neighbor particles adsorbed along a single channel and $2)$ $w_T$, interaction energy between particles adsorbed across nearest-neighbor channels. For $w_L/w_T=0$ and $w_T > 0$, successive planes are uncorrelated, the system is equivalent to the triangular lattice and the well-known $(\sqrt{3} \times \sqrt{3})$ $[(\sqrt{3} \times \sqrt{3})^*]$ ordered phase is found at low temperatures and a coverage, $\theta$, of 1/3 $[2/3]$. In the more general case ($w_L/w_T \neq 0$ and $w_T > 0$), a competition between interactions along a single channel and a transverse coupling between sites in neighboring channels allows to evolve to a three-dimensional adsorbed layer. Consequently, the $(\sqrt{3} \times \sqrt{3})$ and $(\sqrt{3} \times \sqrt{3})^*$ structures "propagate" along the channels and new ordered phases appear in the adlayer. The Monte Carlo technique was combined with the recently reported Free Energy Minimization Criterion Approach (FEMCA), to predict the critical temperatures of the order-disorder transformation. The excellent qualitative agreement between simulated data and FEMCA results allow us to interpret the physical meaning of the mechanisms underlying the observed transitions., Comment: 24 pages, 6 figures

Monte Carlo (MC) simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer two-dimensional gas of repulsive linear $k$-mers on a triangular lattice at coverage $k/(2k+1)$. A low-temperature ordered phase, characterized by a repetition of alternating files of adsorbed $k$-mers separated by $k+1$ adjacent empty sites, is separated from the disordered state by a order-disorder phase transition occurring at a finite critical temperature, $T_c$. The MC technique was combined with the recently reported Free Energy Minimization Criterion Approach (FEMCA), [F. Rom\'a et al., Phys. Rev. B, 68, 205407, (2003)], to predict the dependence of the critical temperature of the order-disorder transformation. The dependence on $k$ of the transition temperature, $T_c(k)$, observed in MC is in qualitative agreement with FEMCA. In addition, an accurate determination of the critical exponents has been obtained for adsorbate sizes ranging between $k=1$ and $k=3$. For $k>1$, the results reveal that the system does not belong to the universality class of the two-dimensional Potts model with $q=3$ ($k=1$, monomers). Based on symmetry concepts, we suggested that the behavior observed for $k=1, 2$ and 3 could be generalized to include larger particle sizes ($k \geq 2$)., Comment: 17 pages, 13 figures

A novel order parameter $\Phi$ for spin glasses is defined based on topological criteria and with a clear physical interpretation. $\Phi$ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson $\pm J$ model on a square lattice, comparing its properties with the usual $q$ order parameter. Finite size scaling procedures are performed. Results and analyses based on $\Phi$ confirm a zero temperature phase transition and allow to identify the low temperature phase. The advantages of $\Phi$ are brought out and its physical meaning is established., Comment: 13 pages, 4 figures, to appear in Physica A