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Unveiling the principles behind self-organization in quantum systems is of paramount importance, both intrinsically and practically, in view of foreseeable technological applications. Recently, increasing attention is being paid to atomic systems in curved geometries, which are a promising platform for the discovery of new emergent phenomena. A notable example is that of a gas of ultracold atoms loaded into a thin spherical shell, according to a protocol introduced by Zobay and Garraway more than twenty years ago. However, gravity prevents a dilute assembly of atoms from uniformly spreading throughout the shell, which explains why experiments on the condensation and superfluidity of bubble-trapped gases are usually conducted in space under microgravity conditions. In this paper, we focus instead on strongly-interacting quantum particles in a bubble trap, choosing the cluster supersolid of soft-core bosons as testbed. To study the impact of gravity on supersolid order, we consider a gedanken experiment in which the strength of gravity relative to the core repulsion is gradually enhanced. Using path integral Monte Carlo simulations, we trace the parallel evolution of system structure and superfluidity at low temperature, finding that the latter is sizeable only when gravity is a small perturbation or, at the other extreme, so strong that particles are all gathered in one cluster at the bottom of the trap. Finally, we assess the relevance of gravity for the equilibrium behavior of ultracold Rydberg-dressed atoms in a bubble trap, concluding that in some cases clues of the supersolid phase in the absence of gravity could be found even in a laboratory on Earth., Comment: 10 pages, 6 figures

Mixed-anion compounds, which incorporate multiple types of anions into materials, displays tailored crystal structures and physical/chemical properties, garnering immense interests in various applications such as batteries, catalysis, photovoltaics, and thermoelectrics. However, detailed studies regarding correlations between crystal structure, chemical bonding, and thermal/vibrational properties are rare for these compounds, which limits the exploration of mixed-anion compounds for associated thermal applications. In this work, we investigate the lattice dynamics and thermal transport properties of the metal chalcohalides, CuBiSCl2. A high-purity polycrystalline CuBiSCl2 sample, successfully synthesized via modified solid-state synthetic method, exhibits a low lattice thermal conductivity of 0.9-0.6 W m-1 K-1 from 300 to 573 K. By combining various experimental techniques including 3D electron diffraction with theoretical calculations, we elucidate the origin of low lattice thermal conductivity in CuBiSCl2. The stereo-chemical activity of the 6s2 lone pair of Bi3+ favors an asymmetric environment with neighboring anions involving both short and long bond lengths. This particularity often implies weak bonding, low structure dimensionality, and strong anharmonicity, leading to low lattice thermal conductivity. In addition, the strong two-fold linear S-Cu-S coordination with weak Cu -- Cl interactions induces large anisotropic vibration of Cu or structural disorder, which enables strong phonon-phonon scattering and decreases lattice thermal conductivity. The investigations into lattice dynamics and thermal transport properties of CuBiSCl2 broadens the scope of the existing mixed-anion compounds suitable for the associated thermal applications, offering a new avenue for the search of low thermal conductivity materials in low-cost mixed-anion compounds.

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this paper, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum Monte Carlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter $\eta$ describing its strength. If $\eta$ exceeds a characteristic value $\eta_c$, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for $\eta\lesssim\eta_c$, finding -- in addition to a liquid-vapor transition -- a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As $\eta$ approaches $\eta_c$, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for $\eta$ larger than $\eta_c$ our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles., Comment: 6 pages, 4 figures

Confinement can have a considerable effect on the behavior of particle systems, and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using Path Integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at soft-core bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical soft-core particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasi-one-dimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. Crucially, this supersolid phase is only slightly disturbed by gravity. We argue that the predicted phases can be revealed in magnetic traps with spherical-shell geometry, possibly even in a lab on Earth. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries., Comment: 16 pages, 10 figures, videos available on request

The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct "phases", The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating "solids", also the existence of supersolid "phases" which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers., Comment: 30 pages, 11 figures

We reconsider model II of [J. Chem. Phys. 1968, 49, 1778--1783], a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: on closer inspection the alleged liquid-vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier to crystal nucleation from the "liquid"., Comment: 26 pages, 10 figures

We use Monte Carlo simulation and the Reference Interaction Site Model (RISM) theory of molecular fluids to investigate a simple model of colloidal mixture consisting of dimers, made up of two tangent hard monomers of different size, and hard spheres. In addition to steric repulsion, the two species interact via a square-well attraction only between small monomers and spheres. Recently, we have characterized the low-temperature regime of this mixture by Monte Carlo, reporting on the spontaneous formation of a wide spectrum of supramolecular aggregates [Prestipino et al, J. Phys. Chem. B, 2019, 123, 9272]. Here we focus on a regime of temperatures where, on cooling, the appearance of local inhomogeneties first, and the early stages of aggregation thereafter, are observed. In particular, we find signatures of aggregation in the onset of a low-wavevector peak in the structure factors of the mixture, as computed by both theory and simulation. Then, we link the structural information to the microscopic arrangement through a detailed cluster analysis of Monte Carlo configurations. In this regard, we devise a novel method to compute the maximum distance for which two spheres can be regarded as bonded together, a crucial issue in the proper identification of fluid aggregates. The RISM theory provides relatively accurate structural and thermodynamic predictions in comparison with Monte Carlo, but with slightly degrading performances as the fluid progresses inside the locally inhomogeneous phase. Our study certifies the efficacy of the RISM approach as a useful complement to numerical simulation for a reasoned analysis of aggregation properties in colloidal mixtures., Comment: 12 pages, 13 figures, 69 references. Accepted for publication in Physical Chemistry Chemical Physics, 2021

We study the self-assembly on a spherical surface of a model for a binary mixture of amphiphilic dimers in the presence of guest particles via Monte Carlo (MC) computer simulation. All particles have a hard core, but one monomer of the dimer also interacts with the guest particle by means of a short-range attractive potential. We observe the formation of aggregates of various shape as a function of the composition of the mixture and of the size of guest particles. Our MC simulations are a further step towards a microscopic understanding of experiments on colloidal aggregation over curved surfaces, such as oil droplets., Comment: 16 pages, 7 figures

Ever since the first observation of Bose-Einstein condensation in the nineties, ultracold quantum gases have been the subject of intense research, providing a unique tool to understand the behavior of matter governed by the laws of quantum mechanics. Ultracold bosonic atoms loaded in an optical lattice are usually described by the Bose-Hubbard model or a variant of it. In addition to the common insulating and superfluid phases, other phases (like density waves and supersolids) may show up in the presence of a short-range interparticle repulsion and also depending on the geometry of the lattice. We herein explore this possibility, using the graph of a convex polyhedron as "lattice" and playing with the coordination of nodes to promote the wanted finite-size ordering. To accomplish the job we employ the method of decoupling approximation, whose efficacy is tested in one case against exact diagonalization. We report zero-temperature results for two Catalan solids, the tetrakis hexahedron and the pentakis dodecahedron, for which a thorough ground-state analysis reveals the existence of insulating "phases" with polyhedral order and a widely extended supersolid region. The key to this outcome is the unbalance in coordination between inequivalent nodes of the graph. The predicted phases can be probed in systems of ultracold atoms using programmable holographic optical tweezers., Comment: 41 pages, 9 figures

I study the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh ("Platonic mesh") and interacting through an extended Bose-Hubbard Hamiltonian. Only the hard-core version of the model is considered here, for two instances of Platonic mesh. Using the mean-field decoupling approximation, I show that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system., Comment: 27 pages, 8 figures

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded on theoretical arguments, that both entropies are extensive quantities., Comment: 31 pages, 3 figures

Building structures with hierarchical order through the self-assembly of smaller blocks is not only a prerogative of nature, but also a strategy to design artificial materials with tailored functions. We explore in simulation the spontaneous assembly of colloidal particles into extended structures, using spheres and size-asymmetric dimers as solute particles, while treating the solvent implicitly. Besides rigid cores for all particles, we assume an effective short-range attraction between spheres and small monomers to promote, through elementary rules, dimer-mediated aggregation of spheres. Starting from a completely disordered configuration, we follow the evolution of the system at low temperature and density, as a function of the relative concentration of the two species. When spheres and large monomers are of same size, we observe the onset of elongated aggregates of spheres, either disconnected or cross-linked, and a crystalline bilayer. As spheres grow bigger, the self-assembling scenario changes, getting richer overall, with the addition of flexible membrane sheets with crystalline order and monolayer vesicles. With this wide assortment of structures, our model can serve as a viable template to achieve a better control of self-assembly in dilute suspensions of microsized particles., Comment: 21 pages, 12 figures

We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic arguments to investigate, within a variational ansatz for the single-particle state, the crossover between distinct finite-size "phases" in the parameter space spanned by the sphere radius and the chemical potential. In particular, for radii up to a few interaction ranges we examine the stability of the fluid phase with respect to a number of crystal-like arrangements having the symmetry of a regular or semi-regular polyhedron. We find that, while quantum fluctuations keep the system fluid at low density, upon compression it eventually becomes inhomogeneous, i.e., particles gather together in clusters. As the radius increases, the nature of the high-density aggregate varies and we observe a sequence of transitions between different cluster phases ("solids"), whose underlying rationale is to maximize the coordination number of clusters, while ensuring at the same time the proper distance between each neighboring pair. We argue that, at least within our mean-field description, every cluster phase is supersolid., Comment: 38 pages, 12 figures

We study a system of penetrable bosons on a line, focusing on the high-density/weak-interaction regime, where the ground state is, to a good approximation, a condensate. Under compression, the system clusterizes at zero temperature, i.e., particles gather together in separate, equally populated bunches. We compare predictions from the Gross-Pitaevskii (GP) equation with those of two distinct variational approximations of the single-particle state, written as either a sum of Gaussians or the square root of it. Not only the wave functions in the three theories are similar, but also the phase-transition density is the same for all. In particular, clusterization occurs together with the softening of roton excitations in GP theory. Compared to the latter theory, Gaussian variational theory has the advantage that the mean-field energy functional is written in (almost) closed form, which enables us to extract the phase-transition and high-density behaviors in fully analytic terms. We also compute the superfluid fraction of the clustered system, uncovering its exact behavior close, as well as very far away from, the transition., Comment: 27 pages, 4 figures

The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function --- represented as a sum of Gaussians --- that is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to predict the order (and sometimes even the location) of the transition. We consider a number of crystal structures in two and three dimensions and determine the phase diagram. Depending on the lattice, the transition from fluid to solid can be first-order or continuous, a lower coordination entailing a milder transition. In two dimensions, crystallization would occur at the same pressure on three distinct lattices (square, honeycomb, and stripes), all providing metastable phases with respect to the triangular crystal. A similar scenario holds in three dimensions, where the simple-cubic and diamond crystals also share a common melting point; however, the stable crystal at low pressure is typically fcc. Upon compression and depending on the shape of the potential, the fcc crystal may transform into hcp. We conclude by sketching a theory of the solid-fluid interface and of quantum nucleation of the solid from the fluid., Comment: 39 pages, 9 figures

We study, by using liquid-state theories and Monte Carlo simulation, the behavior of systems of classical particles interacting through a finite pair repulsion supplemented with a longer range attraction. Any such potential can be driven Ruelle-unstable by increasing the attraction at the expense of repulsion, until the thermodynamic limit is lost. By examining several potential forms, we find that all systems exhibit a qualitatively similar behavior in the fluid phase as the threshold of thermodynamic stability is approached (and possibly surpassed). The general feature underlying the approach to Ruelle instability is a pronounced widening of the liquid-vapor binodal (and spinodal) line at low temperatures, to such an extent that at the stability threshold a vanishing-density vapor would coexist with a diverging-density liquid. We attempt to rationalize the universal pathway to Ruelle instability in soft-core fluids by appealing to a heuristic argument., Comment: 24 pages, 10 figures

Crystallization from a supercooled liquid initially proceeds via the formation of a small solid embryo (nucleus), which requires surmounting an activation barrier. This phenomenon is most easily studied by numerical simulation, using specialized biased-sampling techniques to overcome the limitations imposed by the rarity of nucleation events. Here, I focus on the barrier to homogeneous ice nucleation in supercooled water, as represented by the monatomic-water model, which in the bulk exhibits a complex interplay between different ice structures. I consider various protocols to identify solidlike particles on a computer, which perform well enough for the Lennard-Jones model, and compare their respective impact on the shape and height of the nucleation barrier. It turns out that the effect is stronger on the nucleus size than on the barrier height. As a by-product of the analysis, I determine the structure of the nucleation cluster, finding that the relative amount of ice phases in the cluster heavily depends on the method used for classifying solidlike particles. Moreover, the phase which is most favored during the earlier stages of crystallization may happen, depending on the nucleation coordinate adopted, to be different from the stable polymorph. Therefore, the quality of a reaction coordinate cannot be assessed simply on the basis of the barrier height obtained. I explain how this outcome is possible and why it just points out the shortcoming of collective variables appropriate to simple fluids in providing a robust method of particle classification for monatomic water., Comment: 41 pages, 15 figures

The short range order in Ge$_{30}$Ga$_{5}$Sb$_{10}$Se$_{55}$ and Ge$_{21}$Ga$_{5}$Sb$_{10}$Se$_{64}$ glasses was investigated by X-ray (XRD) and neutron diffraction (ND) as well as extended X-ray absorption fine structure (EXAFS) measurements at the Ge, Ga, Sb and Se K-edges. Large scale structural models were obtained by fitting simultaneously the experimental data sets by reverse Monte Carlo (RMC) simulation technique. It was found that Ge, Sb and Se atoms follow the Mott-rule and have 4, 3 and 2 nearest neighbors, respectively. The average coordination number of the Ga atoms was around 4. The structure of these glasses can be described by the chemically ordered network model: the Ge-Se, Ga-Se and Sb-Se bonds are the most prominent while Ge-Ge and Ge-Sb bonds are formed only in Se-poor compositions. Models generated by RMC contained some long distances (0.3-0.4 {\AA} higher than the usual covalent bond lengths) between Ge-Se and/or Ge-Ge pairs. Dedicated simulation runs confirm the existence of these bonds., Comment: 20 pages, 5 figures, submitted to Journal of Non-Crystalline Solids

A previously unreported Pb-based perovskite PbMoO$_3$ is obtained by high-pressure and high-temperature synthesis. This material crystallizes in the $Pm\bar{3}m$ cubic structure at room temperature, making it distinct from typical Pb-based perovskite oxides with a structural distortion. PbMoO$_3$ exhibits a metallic behavior down to 0.1 K with an unusual $T$-sub linear dependence of the electrical resistivity. Moreover, a large specific heat is observed at low temperatures accompanied by a peak in $C_P/T^3$ around 10 K, in marked contrast to the isostructural metallic system SrMoO$_3$. These transport and thermal properties for PbMoO$_3$, taking into account anomalously large Pb atomic displacements detected through diffraction experiments, are attributed to a low-energy vibrational mode, associated with incoherent off-centering of lone pair Pb$^{2+}$ cations. We discuss the unusual behavior of the electrical resistivity in terms of a polaron-like conduction, mediated by the strong coupling between conduction electrons and optical phonons of the local low-energy vibrational mode., Comment: 5 pages, 5 figures

We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration $\chi$. For low $\chi$ (less than $10\%$), most guests are isolated and coated with a layer of dimers. As $\chi$ progressively increases, clusters grow in size becoming more and more elongated and polydisperse; after reaching a shallow maximum for $\chi\approx 50\%$, the size of clusters again reduces upon increasing $\chi$ further. In one case only ($\chi=50\%$ and moderately low temperature) the mixture relaxed to a fluid of lamellae, suggesting that in this case clusters are metastable with respect to crystal-vapor separation. On heating, clusters shrink until eventually the system becomes homogeneous on all scales. On the other hand, as the mixture is made denser and denser at low temperature, clusters get increasingly larger until a percolating network is formed., Comment: 28 pages, 14 figures

We provide a systematic derivation of boundary layer models in magnetohydrodynamics (MHD), through an asymptotic analysis of the incompressible MHD system. We recover classical linear models, related to the famous Hartmann and Shercliff layers, as well as nonlinear ones, that we call magnetic Prandtl models. We perform their linear stability analysis, emphasizing the stabilizing effect of the magnetic field., Comment: 16 pages

Markov State Modeling has recently emerged as a key technique for analyzing rare events in thermal equilibrium molecular simulations and finding metastable states. Here we export this technique to the study of friction, where strongly non-equilibrium events are induced by an external force. The approach is benchmarked on the well-studied Frenkel-Kontorova model, where we demonstrate the unprejudiced identification of the minimal basis microscopic states necessary for describing sliding, stick-slip and dissipation. The steps necessary for the application to realistic frictional systems are highlighted., Comment: 9 pages, 11 figures

The phase behavior of stabilized dispersions of macromolecules is most easily described in terms of the effective interaction between the centers of mass of solute particles. For molecules like polymer chains, dendrimers, etc., the effective pair potential is {\em finite} at the origin, allowing "particles" to freely interpenetrate each other. Using a double-Gaussian model (DGM) for demonstration, we studied the behavior of the system as a function of the attraction strength $\eta$. Above a critical strength $\eta_{\rm c}$, the infinite-size system is Ruelle-unstable, in that it collapses to a cluster of finite volume. As $\eta_{\rm c}$ is approached from below, the liquid-vapor region exhibits an anomalous widening at low temperature, and the liquid density apparently diverges at the stability threshold. Above $\eta_{\rm c}$, the thermodynamic plane is divided in two regions, differing in the value of the {\em average} waiting time for collapse, being finite and small on one side of the boundary line, while large or even infinite in the other region. Upon adding a small hard core to the DGM potential, stability is fully recovered and the boundary line is converted to the spinodal line of a transition between fluid phases. We argue that the destabilization of a colloidal dispersion, as induced by the addition of salt or other flocculant, finds a suggestive analogy in the process by which a strengthening of the attraction pushes a stabilized-DGM system inside the fluid-fluid spinodal region., Comment: 5 pages, 5 figures

Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively pertain to a finite-size sample in a periodic box, as they are washed out in the bulk limit. Below the critical density, at each pressure jump the shape of the liquid drop undergoes a morphological transition, changing from spherical to cylindrical to slab-like as the density is increased. We formulate a simple theory of these shape transitions, which is adapted from a calculation originally developed by Binder and coworkers [{\em J. Chem. Phys.} {\bf 120}, 5293 (2004)]. Our focus is on the pressure equation of state (rather than on the chemical potential, as in the original work) and includes an extension to elongated boxes. Predictions based on this theory well agree with extensive Monte Carlo data for the cut-and-shifted Lennard-Jones fluid. We further discuss on the thermodynamic stability of liquid drops with shapes other than the three mentioned above, like those found deep inside the liquid-vapor region in simulations starting from scratch. Our theory classifies these more elaborate shapes as metastable., Comment: 14 pages, 8 figures

Phase transitions in one-dimensional classical fluids are usually ruled out by making appeal to van Hove's theorem. A way to circumvent the conclusions of the theorem is to consider an interparticle potential that is everywhere bounded. Such is the case of, {\it e.g.}, the generalized exponential model of index 4 (GEM-4 potential), which in three dimensions gives a reasonable description of the effective repulsion between flexible dendrimers in a solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4 model [S. Prestipino, {\em Phys. Rev. E} {\bf 90}, 042306 (2014)] has recently provided evidence of an infinite sequence of low-temperature cluster phases, however also suggesting that upon pushing the simulation forward what seemed a true transition may eventually prove to be only a sharp crossover. We hereby investigate this problem theoretically, by three different and increasingly sophisticated approaches ({\it i.e.}, a mean-field theory, the transfer matrix of a lattice model of clusters, and the exact treatment of a system of point clusters in the continuum), to conclude that the alleged transitions of the one-dimensional GEM4 system are likely just crossovers., Comment: 18 pages, 9 figures

Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10\% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid., Comment: 17 pages, 12 figures