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

Rodrigues, Nathann T

doi:10.1103/physreve.101.062102

Cited by 4 publications

(3 citation statements)

References 55 publications

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“…The power of the flat histogram method is amplified when applied to densities of states which depend on more than one variable. A viable example is the binary gas, the simplest of which is a mixture of 1-NN and 0-NN particles which shows a nontrivial phase diagram with a tricritical point [81][82][83][84][85][86]. Similarly, multidimensional densities of states appear in HCLG with additional attractive interactions [38,39,[87][88][89].…”

Section: Summary and Discussionmentioning

confidence: 99%

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

et al. 2022

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Hard-core lattice-gas models are minimal models to study entropy-driven phase transitions. In the k-nearestneighbor 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.

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Section: Summary and Discussionmentioning

confidence: 99%

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

et al. 2022

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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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“…Recent examples of systems investigated on these Husimi cacti include frustrated magnets [77], polymers [78] and lattice gases [79]. In particular, quite recently binary [80] and ternary [81] mixtures of kNN particles were analyzed by us on a HL built with cubes.…”

Section: B Husimi Lattice Solutionsmentioning

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

Cited by 4 publications

References 55 publications

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

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

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

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