Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles

Stilck, Jürgen F.

doi:10.1063/1.3658045

Cited by 19 publications

(42 citation statements)

References 18 publications

(28 reference statements)

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“…Flat histogram methods have a significant advantage in being able to access the full phase space in one sweep of the configuration space. The simplest model to study will be the mixture of 1-NN and 0-NN particles which shows a nontrivial phase diagram with a tricritical point [77][78][79][80][81][82][83]. Estimating the critical parameters for the model from the flat histogram method would be a starting point.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2021

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We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hardcore 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.

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Section: Discussionmentioning

confidence: 99%

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

et al. 2021

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“…I. For comparison, results for the BL with coordination q = 4 [84] are also displayed in this table, which can be seen as the "L = 0" case. Since these last values do not follow the systematic convergence observed in the data for L 1, they will not be used in the extrapolations.…”

Section: Critical Parameters For the 1nn Modelmentioning

confidence: 99%

Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases

Rodrigues,

Oliveira

2021

Preprint

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Although lattice gases composed by kNN particles, forbidding up to their kth nearest neighbors of being occupied, have been widely investigated in literature, the location and the universality class of the fluid-columnar transition in the 2NN model on the square lattice is still a topic of debate. Here, we present grand-canonical solutions of this model on Husimi lattices built with diagonal square lattices, with 2L(L + 1) sites, for L 7. The systematic sequence of mean-field solutions confirms the existence of a continuous transition in this system and extrapolations of the critical chemical potential µ2,c(L) and particle density ρ2,c(L) to L → ∞ yield estimates of these quantities in close agreement with previous results for the 2NN model on the square lattice. To confirm the reliability of this approach we employ it also for the 1NN model, where very accurate estimates for the critical parameters µ1,c and ρ1,c -for the fluid-solid transition in this model on the square lattice -are found from extrapolations of data for L 6. The non-classical critical exponents for these transitions are investigated through the coherent anomaly method (CAM), which in the 1NN case yields β and ν differing by at most 6% from the expected Ising exponents. For the 2NN model, the CAM analysis is somewhat inconclusive, because the exponents sensibly depend on the value of µ2,c used to calculate them. Notwithstanding, our results suggest that β and ν are considerably larger than the Ashkin-Teller exponents reported in numerical studies of the 2NN system.

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“…More recently, exacts solutions have been found for some random graphs and also for particles that differ in size [14]. An exact solution on the Bethe lattice has been derived for a model with two kinds of particlessmaller ones which occupy a single lattice site and larger ones which do not allow other particles to occupy its neighbouring sites [15].…”

Section: Introductionmentioning

confidence: 99%

Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

Shapoval,

Dudka,

Bénichou

et al. 2021

Preprint

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We study equilibrium properties of binary lattice-gases comprising A and B particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials µ A = µ B = µ. The particles interact via onsite hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion for AB pairs and interactions of arbitrary strength J, positive or negative, for AA and BB pairs. For tree-like Bethe and Husimi lattices we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for J being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at µ = µ c from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of J, this transition can be either continuous or of the first order. For sufficiently big negative J, the behaviour on the two lattices becomes markedly different: while for the Bethe lattice there exists a continuous transition into a phase with an alternating order followed by a continuous re-entrant transition into a disordered phase, an alternating order phase is absent on the Husimi lattice due to strong frustration effects.

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Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles

Cited by 19 publications

References 18 publications

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

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

Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases

Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

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