Search

We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the minimal energy of such systems. The 2D rectangle lattices we consider have an elementary cell of sides a and b, the aspect ratio is defined as Δ = b / a and the inverse particle density A = a b ; therefore, the “symmetric” state with Δ = 1 corresponds to the square lattice and the “non-symmetric” state to the rectangular lattice with Δ ≠ 1 . For certain types of the interaction potential, by changing continuously the particle density, such lattice systems undertake at a specific value of the (inverse) particle density A ∗ a structural transition from the symmetric to the non-symmetric state. The structural transition can be either of first order (Δ unstick from its symmetric value Δ = 1 discontinuously) or of second order (Δ unstick from Δ = 1 continuously); the first and second-order phase transitions are separated by the so-called tricritical point. We develop a general theory on how to determine the exact values of the transition densities and the location of the tricritical point. The general theory is applied to the double Yukawa and Yukawa–Coulomb potentials. [ABSTRACT FROM AUTHOR]

In this note, we revisit the scaling relations among "hatted critical exponents", which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators. [ABSTRACT FROM AUTHOR]

[011]-oriented unpoled relaxor ferroelectric Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 crystals are studied by means of acoustic emission and dielectric methods in dependence on both temperature and dc bias electric field. The rhombohedral-cubic ferroelectric phase transition and the dielectric maximum as well as the intermediate temperature are successfully detected. Both rhombohedral-cubic ferroelectric phase transition and the dielectric maximum are studied in dependence on dc bias electric field, too. No the critical end point, but the tricritical one is detected. Existence of the supercritical behavior is discussed in these crystals. [ABSTRACT FROM AUTHOR]

The phase diagrams of spin-1 Blume-Capel (BC) model under the constraints of bimodal random crystal and trimodal random magnetic fields are investigated by employing the lowest approximation of the cluster variation method (LACVM). The crystal field is either turned on with probability 1 - q or turned off with q, while the magnetic field is either turned off with probability p or turned on up or down for the chosen axis with (1 - p) / 2 randomly. The phase diagrams are calculated by exploiting the thermal variations of the order-parameters on the (D / J , k B T / J) , (p , k B T / J) , (q , k B T / J) and (h / J , k B T / J) planes. It is found that the model presents first- and second-order transitions, a few types of the critical temperatures including the tricritical points. It also exhibits reentrant behavior, i.e. double second-order phase transitions. [ABSTRACT FROM AUTHOR]

Using the two-site cluster mean-field method and the concept of negativity, the magnetization and entanglement of spin-1 quantum ferromagnetic Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions on d-dimensional ( d = 1 , 2 , 3 , 4 ) lattices are studied. The phase transitions and the variations of the negativity with temperature, anisotropy and DM interaction parameters are obtained. It is found that in the systems there are both second-order, first-order phase transitions and tricritical points. For the one-dimensional system, there is a maximum value of the negativity at a certain temperature which corresponds to the phase transition point for the case of first-order phase transition, and the maximum value increases with the increase of the DM interaction intensity. We also find that for two-dimensional square lattice with different temperature values, negativity increases with increasing DM interaction, and finally approaches to the same value. There is a lower limit of the DM interaction intensity (or temperature) above which negativity exists. In addition, we discuss the effect of the dimension on the magnetization, negativity and tricritical point. The results show that the tricritical temperature is independent of the exchange anisotropy parameter Δ , and the lower the dimension, the more obvious the quantum effect. [ABSTRACT FROM AUTHOR]

In this note, we revisit the scaling relations among “hatted critical exponents”, which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.

In this work, the thermodynamic and magnetic properties such as total and partial magnetizations, magnetic susceptibility, internal energy, total specific heat, magnetic hysteresis loops and compensation temperature of a ferrimagnetic mixed spins-3/2 and spins-5/2 hexagonal Ising nanowire, have been determined by using Monte Carlo method based on the Metropolis algorithm. The effects of the longitudinal crystal field, the exchange interactions and the temperature on the magnetic properties and hysteresis loops are examined in detail for different values of the system parameters. Moreover, different interesting magnetic phenomena were obtained, such as the seven and triple hysteresis loops at low temperatures, the tricritical point and compensation behavior under certain physical parameters were detected. Our results are also compared with some experimental and theoretical results. [ABSTRACT FROM AUTHOR]

Recent theoretical and experimental studies have shown that ferromagnetic quantum criticality is always avoided in clean systems. Two possibilities have been identified. In the first scenario, the ferromagnetic transition becomes of the first order at a tricritical point before being suppressed. A wing structure phase diagram is observed indicating the possibility of a new type of quantum critical point under magnetic field. In a second scenario, a transition to a modulated magnetic phase occurs. Our recent studies on the compound LaCrGe3 illustrate a third scenario where not only a new magnetic phase occurs, but also a change of order of the transition at a tricritical point leading to a wing-structure phase diagram. Careful experimental study of the phase diagram near the tricritical point also illustrates new rules near this type of point.

Recent theoretical and experimental studies have shown that ferromagnetic quantum criticality is always avoided in clean systems. Two possibilities have been identified. In the first scenario, the ferromagnetic transition becomes of the first order at a tricritical point before being suppressed. A wing structure phase diagram is observed indicating the possibility of a new type of quantum critical point under magnetic field. In a second scenario, a transition to a modulated magnetic phase occurs. Our recent studies on the compound LaCrGe3 illustrate a third scenario where not only a new magnetic phase occurs, but also a change of order of the transition at a tricritical point leading to a wing-structure phase diagram. Careful experimental study of the phase diagram near the tricritical point also illustrates new rules near this type of point.

Intensive investigations of PbZr1-xTixO3 (PZT) materials with the ABO3 perovskite structure are connected with their extraordinary piezoelectric properties. Especially well known are PZT ceramics at the Morphotropic Phase Boundary (MPB), with x~0.48, whose applications are the most numerous among ferroelectrics. These piezoelectric properties are often obtained by doping with various ions at the B sites. Interestingly, we have found similar properties for undoped PZT single crystals with low Ti content, for which we have confirmed the existence of the tricritical point near x~0.06. For a PbZr0.95 ± 0.01Ti0.05∓ 0.01O3 crystal, we describe the ultrahigh strain, dielectric, optical and piezoelectric properties. We interpret the ultrahigh strain observed in the region of the antiferroelectric–ferroelectric transition as an inverse piezoelectric effect generated by the coexistence of domains of different symmetries. The complex domain coexistence was confirmed by determining optical indicatrix orientations in domains. The piezoelectric coefficient in this region reached an extremely high value of 5000 pm/V. We also verified that the properties of the PZT single crystals from the region near the tricritical point are incredibly susceptible to a slight deviation in the Ti content. [ABSTRACT FROM AUTHOR]

The distinctive characteristics of water, evident in its thermodynamic anomalies, have implications across disciplines from biology to geophysics. Considered a valid hypothesis to rationalize its unique properties, a liquid-liquid phase transition in water below the freezing point, in the so-called supercooled regime, has nowadays been observed in several molecular dynamics simulations and is being actively researched experimentally. The hypothesis of ferroelectric phase transition in supercooled water can be traced back to 1977, due to Stillinger. In this work, we highlight intriguing and far-reaching implications of water: The ferroelectric and liquid-liquid phase transitions can be designed as two facets of the same underlying phenomenon. Our results are based on the analysis of extensive molecular dynamics simulations and are explained in the context of a classical density functional theory in mean-field approximation valid for a polar liquid, where dipolar interaction is treated perturbatively. The theory underpins the potential role of ferroelectricity in promoting the liquid-liquid phase transition, being the density-polarization coupling inherent in the dipolar interaction potential. The existence of ferroelectric order in supercooled low-density liquid water is confirmed by the observation in molecular dynamics simulations of collective modes in space-time polarization correlation functions, traceable to spontaneous breaking of continuous rotational symmetry. Our work sheds light on water's supercooled behavior and opens the door to experimental investigations of the static and dynamic behavior of water's polarization., Competing Interests: Competing interests statement:The authors declare no competing interest.

The phase transitions in the 5-state 3d site-diluted Potts model are investigated by means of the computer simulation methods. We address systems with liner sizes L × L × L = N, L = 20 ÷ 160 at p = 1.00, 0.90, 0.85, and 0.80. Based on the analysis of the fourth-order Binder cumulants and the histogram data analysis, the position of the tricritical point at the phase diagram is determined. [ABSTRACT FROM AUTHOR]

We used standard Monte Carlo simulations to investigate the magnetic properties of a spin-1 Ising multilayer system composed of two non-equivalent planes A and B, where B being site-diluted. Antiferromagnetic interlayer and ferromagnetic intralayer spin couplings have been considered. Our calculations indicated the occurrence of a compensation phenomenon where the magnetization vanishes before the critical temperature. The effects of various model parameters on the system magnetic properties have been examined in detail and presented in the form of phase diagrams. The results bore some resemblance with those reported in some previous works on systems with or without site-dilution. Depending on values of the spin concentration parameterP the model displayed first- and second-order phase boundaries with the existence of a tricritical point. [ABSTRACT FROM AUTHOR]

In high-resolution adiabatic scanning calorimetry (ASC) experiments, data for the temperature dependence of the specific enthalpy, h(T), and of the specific heat capacity, cp(T), are simultaneously obtained, from which the order of the phase transition and critical behaviour can be evaluated. ASC was applied to study the nematic to ferroelectric nematic phase transition (N–NF) in the liquid crystal molecule 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). The N–NF was found to be very weakly first order with a latent heat Δh = 0.115 ± 0.005 J/g. The pretransitional specific heat capacity behaviour is substantially larger in the high-temperature N phase than in the low-temperature NF phase. In both phases the power-law analysis of cp(T) resulted in a critical exponent α = 0.50 ± 0.05 and amplitude ratio ANF/AN = 0.42 ± 0.03. The very small latent heat and the value of α indicate that the N–NF transition is close to a tricritical point. This is confirmed by a value of the order parameter exponent β ≈ 0.25, recently obtained from electric polarisation measurements. Invoking two-scale-factor universality, it follows from the low value of ANF/AN ratio that the size of the critical fluctuations is much larger in the NF phase than in the N phase. [ABSTRACT FROM AUTHOR]

We provide a pedagogical argument on classical critical behaviors of polymer mixtures, which include an ordinary critical point and several multicritical points such as tricritical, isotropic Lifshitz, and isotropic Lifshitz tricritical points. Various scaling exponents and singularities near those critical points are first derived through analyzing Landau free energies in general but suitable forms. A simple binary blend of A and B homopolymers in the mean-field picture is taken as an example of the ordinary critical point to verify its critical exponents and scaling laws by formulating its Landau free energy with the explicit vertex coefficients. A ternary blend consisting of A and B homopolymers of the same sizes and also symmetric A-B diblock copolymer is then employed to get the classical critical exponents and scaling laws for the multicritical points through directly evaluating phase equilibria and scattering functions with varying chain length ratios. In addition, the validity of the mean-field description in the vicinity of those critical points is discussed based on Ginzburg criteria and upper critical dimensions. [ABSTRACT FROM AUTHOR]

Intensive investigations of PbZr1-xTixO3 (PZT) materials with the ABO3 perovskite structure are connected with their extraordinary piezoelectric properties. Especially well known are PZT ceramics at the Morphotropic Phase Boundary (MPB), with x~0.48, whose applications are the most numerous among ferroelectrics. These piezoelectric properties are often obtained by doping with various ions at the B sites. Interestingly, we have found similar properties for undoped PZT single crystals with low Ti content, for which we have confirmed the existence of the tricritical point near x~0.06. For a PbZr0.95 ± 0.01Ti0.05∓ 0.01O3 crystal, we describe the ultrahigh strain, dielectric, optical and piezoelectric properties. We interpret the ultrahigh strain observed in the region of the antiferroelectric–ferroelectric transition as an inverse piezoelectric effect generated by the coexistence of domains of different symmetries. The complex domain coexistence was confirmed by determining optical indicatrix orientations in domains. The piezoelectric coefficient in this region reached an extremely high value of 5000 pm/V. We also verified that the properties of the PZT single crystals from the region near the tricritical point are incredibly susceptible to a slight deviation in the Ti content.

The maximum electromechanical property of piezoelectric ceramic is normally achieved at morphotropic phase boundary. Herein, we found that a maximum electrostrain is obtained in single rhombohedral phase region at the tricritical point (which is a single rhombohedral phase at room temperature) for BaTi1−xHfxO3 ceramics. The mechanism for electrostrain enhancement at tricritical point (TTP) was uncovered by analyzing its crystallographic feature. The results show that TTP (x = 0.11) exhibits largest electrostrain (S = 0.063%) at room temperature. And the TTP reveals a maximum crystallite size (66.3 nm) and minimum lattice strain (0.7 × 10−4). Further Raman results demonstrate a lowest Raman intensity occurs at TTP, which confirmed the specific crystallographic behavior. Therefore, a minimum lattice strain-induced low elastic energy could lower landau free energy, which is responsible for electrostrain enhancement at TTP. This work may provide a new insight for understanding and designing large electromechanical ceramics. [ABSTRACT FROM AUTHOR]

The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable, metastable and unstable branches of the order parameters are obtained. According to the stable conditions at critical point, we find that the systems exhibit tricritical points. With crystal field and biquadratic interactions, the system has rich phase diagrams with single reentrant or double reentrant phase transitions for appropriate ranges of the both parameters. [ABSTRACT FROM AUTHOR]

We consider temperature-driven phase transitions occurring in a liquid crystal suspension of ferromagnetic particles within the Landau–de Gennes theory. The temperature dependences of the order parameters in the uniaxial model with a vector order parameter for the magnetic subsystem are obtained. The dimensionless expression for the free energy density of the suspension has been used for the study of the phase behavior general regularities of the system. Phase state diagrams of the suspension and temperature dependences of the order parameters of the liquid crystal and the ensemble of magnetic particles for different values of the phenomenological expansion coefficients are constructed. It is shown that the considered model admits the existence of a cascade of temperature phase transitions: isotropic phase–superparamagnetic nematic phase–ferromagnetic nematic phase. We have shown that in the mesomorphic state of the liquid crystal, the spontaneous magnetization can appear in a continuous way or by a jump with decreasing temperature, which corresponds to the tricritical behavior. The values of temperature and expansion coefficients corresponding to the tricritical and triple points are numerically found.

Abstract We investigate phase transitions and critical behaviors in the frustrated J 1 – J 2 – J 3 transverse Ising antiferromagnet on a honeycomb lattice using an effective-field theory. We find that at large negative J 3 ∕ | J 1 | (< − 1 ∕ 3) there is a tricritical point on the phase boundary between Néel antiferromagnetic and paramagnetic phases, in contrast to the corresponding frustrated counterpart with J 3 = 0 and zero transverse field Ω. In particular, the variation of the tricritical point with R = J 2 ∕ | J 1 | and Ω ∕ | J 1 | in the three-dimensional space is constructed for J 3 ∕ | J 1 | = − 0. 4. We also discuss longitudinal and transverse magnetizations calculated within the effective-field approach for J 3 ∕ | J 1 | = − 0. 4 and selected values of R = J 2 ∕ | J 1 | and Ω ∕ | J 1 |. Highlights • We investigate frustrated transverse Ising antiferromagnet on a honeycomb lattice. • We present a ground-state phase diagram as a function of the frustration parameter. • We present the phase diagram of the model by using an effective-field theory. • We discuss temperature dependences of longitudinal and transverse magnetizations. [ABSTRACT FROM AUTHOR]

The structure, dielectric and piezoelectric properties of (1-2x) BiScO3-xPbTiO3-xPbMg1/3Nb2/3O3 ceramics with x = 0.30-0.46 were investigated. A nonmonotonic U-shape behavior of the concentration dependence of the Curie temperature was observed. It was shown that the values of the piezoelectric coefficient d33 of the solid solution with x = 0.42 exceed those for the known BiScO3-PbTiO3-based ceramics. A conclusion was made about the possibility of application of these solid solutions in piezoelectric devices which operate at room temperature. [ABSTRACT FROM AUTHOR]

The Blume-Capel model with mixed spins S = 1 and S = 2, on d-dimensional hypercubic lattice, is studied using the real space renormalization group approximation and specifically the Migdal-Kadanoff technique. We give the phase diagrams on the (Δ1/|J|, 1/|J|) and (Δ2/|J|, 1/|J|) planes which are studied for selected values of Δ2/|J| and Δ1/|J| respectively, with first and second order phase transitions and tricritical points. Also, the associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. In particular, we find that the system under study may exhibit reentrant phenomenon. [ABSTRACT FROM AUTHOR]

We investigate the thermodynamic properties of the zero-field Blume–Capel model in the vicinity of its tricritical point (TCP). We calculate the internal energy, entropy, magnetization, quadrupole moment densities, and their response functions (specific heat and susceptibility) by employing an exact numerical recursion procedure for the model defined in a hierarchical lattice of fractal dimension d. We explore the scaling behavior of the isothermal and constant crystal-field-specific heat as a function of the temperature and the reduced crystal-field parameter along the ferromagnetic and the ordered paramagnetic phase frontier. Results achieved for systems with dimensions d = 2 and 3 exhibit the main features of the continuous and first-order transitions in the TCP neighborhoods. We also probe the phase coexistence in the λ diagram and the latent heat in the neighborhood of the tricritical points locus. • The thermodynamics of the Blume–Capel model is studied near its tricritical point. • The exact local quadrupolar density, internal energy, and entropy are calculated. • The quadrupolar susceptibility and specific heat are studied by finite-size scaling. • Quadrupolar susceptibility and specific heat exhibit a clear first-order transition. • The λ diagram, entropy, and latent heat are probed near the TCP locus. [ABSTRACT FROM AUTHOR]

The topological ferromagnet CoS 2 exhibits an anhysteretic, weakly first-order transition at the Curie temperature of 119.8 K with a tricritical point µ 0 H tcp at 0.034 T. Magnetic symmetry and the mixing of majority and minority spin e g bands at a subband crossing just above the Fermi level produce a topological component of the magnetization that leads to a negative M 3 term in the Landau free energy. The position of the Fermi level relative to the subband crossing is critical for controlling the order of the transition. Hole doping in Co 0.89 Fe 0.11 S 2 drains the minority-spin e g pocket and results in a normal second-order phase transition. Electron doping in Co 0.94 Ni 0.06 S 2 raises the Fermi level toward the subband gap, producing a strongly first-order transition with 15 K hysteresis. Our results demonstrate a relation between topological electronic structure and thermal hysteresis at the Curie point, which may help in the search for magnetocaloric materials.

The critical behavior of the Ising model in the presence of a random magnetic field is investigated for any temperature T . The random field is drawn from the proposed shifted bimodal probability distribution P ( h i ) = ( 1 2 + 1 2 h 0 ) h i δ ( h i − h 0 ) + ( 1 2 − 1 2 h 0 ) h i δ ( h i + h 0 ) , h i is the random field variable with strength h 0 . By obtaining data for several transition temperatures T and random field strengths h 0 , we conclude that the system possesses first and second order phase transitions, joined smoothly at a tricritical point, with coordinates ( T T C P , h 0 T C P , V 0 T C P ) = ( 1 . 5775571 , 3 . 7348565 , − 4 . 7741775 ) , where V 0 is an auxiliary field. Using the variational principle, we determine the phase diagram and the equilibrium equation for magnetization (with zero and nonzero values), solve it for both transitions and at the tricritical point and examine the stability conditions of each phase transition. [ABSTRACT FROM AUTHOR]

Abstract We present a study of the XY vectorial generalization of the Blume–Emery–Griffiths model on the Kagome lattice. Its thermodynamical properties are analyzed for different values of the Hamiltonian parameters by employing extensive and up to date Monte Carlo simulation methods consisting of hybrid algorithms. The results show a phase diagram with Berezinskii–Kosterlitz–Thouless (BKT) transitions, BKT endpoints, and isolated critical or tricritical points. We also compare the phase diagram with previous works on square and triangular lattices and we note that they are qualitatively similar. In addition, we observed that the ratio of the temperature of BKT endpoints to the corresponding BKT temperature of the pure system is a quantity almost independent of the lattice topology. Highlights • It treats the XY Vector Blume–Emery–Griffiths model on a Kagome lattice. • Tricritical points or BKT endpoints and isolated critical points are present on the phase diagram for a range of model parameters. • We compare the phase diagram with previous works and we observed that the ratio of the temperature of BKT endpoints and the BKT temperature of the pure system is a quantity independent of the lattice used. [ABSTRACT FROM AUTHOR]

The phase diagrams and the magnetic properties of a spin-1 Blume-Capel nanoisland are investigated by the use of the effective-field theory based on the probability distribution technique. The influence of the random crystal field and the system parameters on the critical behaviors of the nanoisland are examined. The results show that the system can exhibit a first-order phase transition, a tricritical point, and a re-entrant or even a double re-entrant phenomenon. [ABSTRACT FROM AUTHOR]

Recent theoretical and experimental studies have shown that ferromagnetic quantum criticality is always avoided in clean systems. Two possibilities have been identified. In the first scenario, the ferromagnetic transition becomes of the first order at a tricritical point before being suppressed. A wing structure phase diagram is observed indicating the possibility of a new type of quantum critical point under magnetic field. In a second scenario, a transition to a modulated magnetic phase occurs. Our recent studies on the compound LaCrGe 3 illustrate a third scenario where not only a new magnetic phase occurs, but also a change of order of the transition at a tricritical point leading to a wing-structure phase diagram. Careful experimental study of the phase diagram near the tricritical point also illustrates new rules near this type of point. [ABSTRACT FROM AUTHOR]

In this work, we have focused on the random crystal field effects on the phase diagrams of the mixed spin-1 and spin-5/2 Ising system obtained by utilizing the exact recursion relations (ERR) on the Bethe lattice (BL). The distribution function P ( D i ) = p δ [ D i − D ( 1 + α ) ] + ( 1 − p ) δ [ D i − D ( 1 − α ) ] is used to randomize the crystal field.The phase diagrams are found to exhibit second- and first-order phase transitions depending on the values of α , D and p . It is also observed that the model displays tricritical point, isolated point, critical end point and three compensation temperatures for suitable values of the system parameters. [ABSTRACT FROM AUTHOR]

Magnetic nature of Gd 3 Co is investigated using detailed measurements of temperature and field dependent magnetization. The antiferromagnetic phase is field-instable due to prevailing ferromagnetic exchange correlations above Néel temperature T N ∼ 130 K . Below T N , with gradually increasing magnetic fields, the compound undergoes a quasi-first order phase transition from AFM to spin-flop over region and eventually acquires ferromagnetic phase in higher fields. Further the point at which the quasi-first order transition ends and second order transition sets in is the tricritical point, T TCP ∼ 125.6 K , H TCP ∼ 4.4 kOe . [ABSTRACT FROM AUTHOR]