A Lattice Model of a Classical Hard Sphere Gas: II

Burley, D.M.

doi:10.1088/0370-1328/77/2/328

Cited by 45 publications

(24 citation statements)

References 10 publications

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“…The critical exponents of the three-dimensional Ising model have been estimated, β/ν = 0.518 (7) and γ/ν = 1.9828(57) [32]. These values do not agree with our results of the hard-sphere lattice gas.…”

Section: Discussioncontrasting

confidence: 87%

“…A continuous phase transition occurs at a critical activity. There are many studies of the system by various methods: series expansions [1,2,3,4,5], finite-size scaling and transfer matrix [6], Bethe and ring approximations [7], transfer matrix [8,9,10], corner transfer matrix and series expansions [11], exact calculations [12], and Monte Carlo simulations [13,14]. The critical activity is obtained on various lattice.…”

Section: Introductionmentioning

confidence: 99%

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Critical phenomena of the hard-sphere lattice gas on the simple cubic lattice

Yamagata

1995

Physica A: Statistical Mechanics and its Applications

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Running title Critical phenomena of hard-sphere lattice gas Keywords Hard-sphere lattice gas, Critical phenomena, Monte Carlo method PACS classification codes 02.70.Lq, 64.60.Cn, 68.35.Rh AbstractWe study the critical phenomena of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion by the Monte Carlo method. We get the critical exponents, β/ν = 0.313(9) and γ/ν = 2.37(2), where β is the critical exponent for the staggered density, γ for the staggered compressibility, and ν for the correlation length.

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Section: Discussioncontrasting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Critical phenomena of the hard-sphere lattice gas on the simple cubic lattice

Yamagata

1995

Physica A: Statistical Mechanics and its Applications

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“…This system, which can also interpreted either as 45 o tilted hard-squares of linear size λ = √ 2 or as hard disks of radius √ 2/2, has been extensively studied and here we present some results for the sake of both completeness and comparison. Many different approaches have been used to describe its properties on a square lattice: series expansions [3,5,11,12,13], cluster variational and transfer matrix methods [5,14,15,16,17,18,19,20,21,22,23], renormalization group [24,25], Monte Carlo simulations [26,27,28,29,30,31,32,33], Bethe lattice [5,34,35,36,37,38], and more recently density functional theory [39]. Moreover, this model has also been considered because of its interesting mathematical [40,41,42] and dynamical [43,44,45,46,47,48,49,50,51,…”

Section: A Nearest Neighbor Exclusion (1nn)mentioning

confidence: 99%

Monte Carlo simulations of two-dimensional hard core lattice gases

Fernandes

Arenzon

Levin

2007

The Journal of Chemical Physics

134

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Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, λ (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class -contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.

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“…II for a precise definition for the model). Introduced by Domb and Burley in the 1950s [19][20][21], the k-NN HCLG model has found applications in diverse areas of research. Examples include adsorption on surfaces [22][23][24][25][26][27][28][29], limiting cases of spin models [30][31][32], frustrated antiferromagnets at high magnetic fields [33,34], glass transitions on square [35,36] and Bethe lattices [37], and the study of two-dimensional Rydberg gases [38] and in combinatorial problems [39] such as the unfriendly theater sitting problem [40], the random independent set problem on graphs [41], loss networks [42], q-coloring graphs [43], and reconstruction problems [44].…”

Section: Introductionmentioning

confidence: 99%

Multiple phase transitions in extended hard-core lattice gas models in two dimensions

Nath

Rajesh

2014

Phys. Rev. E

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We study the k-NN hard-core lattice gas model in which the first k next-nearest-neighbor sites of a particle are excluded from occupation by other particles on a two-dimensional square lattice. This model is the lattice version of the hard-disk system with increasing k corresponding to decreasing lattice spacing. While the hard-disk system is known to undergo a two-step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high-density expansions of the free energy and density, we argue that for k = 4,10,11,14,⋯, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for k = 4,...,11. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first-order transition.

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A Lattice Model of a Classical Hard Sphere Gas: II

Cited by 45 publications

References 10 publications

Critical phenomena of the hard-sphere lattice gas on the simple cubic lattice

Critical phenomena of the hard-sphere lattice gas on the simple cubic lattice

Monte Carlo simulations of two-dimensional hard core lattice gases

Multiple phase transitions in extended hard-core lattice gas models in two dimensions

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