Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly

Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor

Hard-core lattice-gas models are minimal models to study entropy-driven phase transitions. In the k-nearest-neighbor lattice gas, a particle excludes all sites up to the kth next-nearest neighbors from being occupied by another particle. As k increases from one, it extrapolates from nearest-neighbor exclusion to the hard-sphere gas. In this paper we study the model on the triangular lattice for k≤7 using a flat histogram algorithm that includes cluster moves. Earlier studies focused on k≤3. We show that for 4≤k≤7, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and nonconvexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.

Weakly first-order transition in an athermal lattice gas

We investigate the phase behavior of a two-dimensional athermal lattice gas in which every hard-core particle can have two or fewer nearest neighboring occupied sites on the square lattice. The ground state and close packing density are determined and it is found that at large chemical potential the model undergoes an ordering phase transition with preferential sublattice occupation. Although near the transition point the particle density and entropy exhibit an apparent discontinuity, we find that the order parameter and fluctuations of thermodynamic quantities do not scale with the system volume. These paradoxical results are reconciled by analyzing the size-dependent flow of the thermal exponent by phenomenological renormalization and the curve-crossing method, which lead to a weakly first-order phase transition scenario.

First-order phase transition in a two dimensional BM3 model

The phase behavior of a Biroli–Mézard model on the two dimensional square lattice in which hard-core particles can have at most three nearest neighboring occupied sites is investigated by means of grand-canonical Monte Carlo simulations. Finite-size scaling analysis of relevant thermodynamic quantities obtained via the histogram reweighting technique reveals that at high-density, the model undergoes a first-order phase transition with preferential sublattice occupation to a crystal phase with enantiomorph ground state configurations, in close analogy to the hard-core lattice gas with the exclusion range extended up to the third shell of nearest neighbors.

Phase diagram and critical properties of a two-dimensional associating lattice gas

We revisit the associating lattice gas (ALG) introduced by Henriques et al. [Phys. Rev. E 71, 031504 (2005)PLEEE81539-375510.1103/PhysRevE.71.031504] in its symmetric version. In this model, defined on the triangular lattice, interaction between molecules occupying nearest-neighbor sites depends on their relative orientation, mimicking the formation of hydrogen bonds in network-forming fluids. Although all previous studies of this model agree that it has a disordered fluid (DF), a low-density liquid (LDL), and a high-density liquid (HDL) phase, quite different forms have been reported for its phase diagram. Here, we present a thorough investigation of its phase behavior using both transfer matrix calculations and Monte Carlo (MC) simulations, along with finite-size scaling extrapolations. Results in striking agreement are found using these methods. The critical point associated with the DF-HDL transition at full occupancy, identified by Furlan et al. [Phys. Rev. E 100, 022109 (2019)2470-004510.1103/PhysRevE.100.022109] is shown to be one terminus of a critical line separating these phases. In opposition to previous simulation studies, we find that the transition between the DF and LDL phases is always discontinuous, similar to the LDL-HDL transition. The associated coexistence lines meet at the point where the DF-HDL critical line ends, making it a critical-end-point. Overall, the form of the phase diagram observed in our simulations is very similar to that found in the exact solution of the model on a Husimi lattice. Our results confirm that, despite the existence of some waterlike anomalies in this model, it is unable to reproduce key features of the phase behavior of liquid water.

Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases

We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hard-core lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first k next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for k=1,2,3 both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.

Adsorption kinetics and thermodynamic properties of a binary mixture of hard-core particles on a square lattice

The adsorption kinetics and thermodynamic properties of a binary mixture on a square lattice are studied using the random sequential adsorption with surface diffusion (RSAD). We compare the adsorption of binary species with different equilibrium rate constants and effective rates of adsorption to a surface and find that the temporal evolution of surface coverages of both species can be obtained through the use of the blocking function of a system with irreversible adsorption of highly diffusive particles. Binary mixtures, when one of the components follows the random sequential adsorption (RSA) without surface diffusion and the other follows the RSAD model, display competitive adsorption in addition to cooperative phenomena. Specifically, (i) species replacement occurs over a long period of time, while the total coverage remains unchanged after a short time, (ii) the presence of the RSAD component shifts the jamming coverage to the higher values, and (iii) the maximum jamming coverage is obtained when the effective adsorption of the RSA type components is lower than the other adsorbing particles.

Fluid-fluid demixing and density anomaly in a ternary mixture of hard spheres

We report the grand-canonical solution of a ternary mixture of discrete hard spheres defined on a Husimi lattice built with cubes, which provides a mean-field approximation for this system on the cubic lattice. The mixture is composed of pointlike particles (0NN) and particles which exclude up to their first (1NN) and second neighbors (2NN), with activities z_{0}, z_{1}, and z_{2}, respectively. Our solution reveals a very rich thermodynamic behavior, with two solid phases associated with the ordering of 1NN (S1) or 2NN particles (S2), and two fluid phases, one being regular (RF) and the other characterized by a dominance of 0NN particles (F0 phase). However, in most part of the phase diagram these fluid (F) phases are indistinguishable. Discontinuous transitions are observed between all the four phases, yielding several coexistence surfaces in the system, among which a fluid-fluid and a solid-solid demixing surface. The former one is limited by a line of critical points and a line of triple points (where the phases RF-F0-S2 coexist), both meeting at a special point, after which the fluid-fluid coexistence becomes metastable. Another line of triple points is found, connecting the F-S1, F-S2, and S1-S2 coexistence surfaces. A critical F-S1 surface is also observed meeting the F-S1 coexistence one at a line of tricritical points. Furthermore, a thermodynamic anomaly characterized by minima in isobaric curves of the total density of particles is found, yielding three surfaces of minimal density in the activity space, depending on which activity is kept fixed during its calculation.

Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes

We study binary mixtures of hard particles, which exclude up to their kth nearest neighbors (kNN) on the simple cubic lattice and have activities z_{k}. In the first model analyzed, point particles (0NN) are mixed with 1NN ones. The grand-canonical solution of this model on a Husimi lattice built with cubes unveils a phase diagram with a fluid and a solid phase separated by a continuous and a discontinuous transition line which meet at a tricritical point. A density anomaly, characterized by minima in isobaric curves of the total density of particles against z_{0} (or z_{1}), is also observed in this system. Overall, this scenario is identical to the one previously found for this model when defined on the square lattice. The second model investigated consists of the mixture of 1NN particles with 2NN ones. In this case, a very rich phase behavior is found in its Husimi lattice solution, with two solid phases-one associated with the ordering of 1NN particles (S1) and the other with the ordering of 2NN ones (S2)-beyond the fluid (F) phase. While the transitions between F-S2 and S1-S2 phases are always discontinuous, the F-S1 transition is continuous (discontinuous) for small (large) z_{2}. The critical and coexistence F-S1 lines meet at a tricritical point. Moreover, the coexistence F-S1,F-S2, and S1-S2 lines meet at a triple point. Density anomalies are absent in this case.

Columnar-disorder phase boundary in a mixture of hard squares and dimers

A mixture of hard squares, dimers, and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to a high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes a Kosterliz-Thouless-type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.