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

Nath, Trisha; Rajesh, R.

doi:10.1103/physreve.90.012120

Cited by 44 publications

(77 citation statements)

References 97 publications

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“…The calculation of these probabilities reduces to a one dimensional problem which may be solved exactly (see Refs. [20,39,45] for details). The evaporation and deposition move satisfies detailed balance as the transition rates depend only on the equilibrium probabilities of the new configuration.…”

Section: Model Description and Monte-carlo Algorithmmentioning

confidence: 99%

Different phases of a system of hard rods on three dimensional cubic lattice

2017

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We study the different phases of a system of monodispersed hard rods of length k on a cubic lattice using an efficient cluster algorithm which can simulate densities close to the fully-packed limit. For k ≤ 4, the system is disordered at all densities. For k = 5, 6, we find a single density-driven transition from a disordered phase to high density layered-disordered phase in which the density of rods of one orientation is strongly suppressed, breaking the system into weakly coupled layers. Within a layer, the system is disordered. For k ≥ 7, three density driven transitions are observed numerically: isotropic to nematic to layered-nematic to layered-disordered. In the layered-nematic phase, the system breaks up into layers, with nematic order in each in each layer, but very weak correlation between the ordering direction between different layers. We argue that the layered-nematic phase is a finite-size effect, and in the thermodynamic limit, the nematic phase will have higher entropy per site.

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Section: Model Description and Monte-carlo Algorithmmentioning

confidence: 99%

Different phases of a system of hard rods on three dimensional cubic lattice

2017

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“…Although the lattice gas model has been studied extensively in the literature, only the single case of a triangular lattice with first neighbor exclusion was solved exactly, by Baxter [31]. For all other variants, a number of lattice gas methods have been developed over years based on various approximation methods: the matrix method of Kramer and Wannier [32][33][34][35][36][37][38], the density (or activity) series expansion method [32,33,[39][40][41][42][43] , the generalized Bethe method [44][45][46], Monte Carlo simulation [37,[47][48][49][50][51], the Rushbrooke and Scoins method [52] and fundamental measure theory [53]. Despite all of this effort, the lattice gas model is not able to describe the adsorption isotherm of the system, and instead focuses on the equation of state and the nature of phase transition.…”

Section: Introductionmentioning

confidence: 99%

Liquid-hexatic-solid phase transition of a hard-core lattice gas with third neighbor exclusion

Darjani

Koplik

Banerjee

et al. 2019

The Journal of Chemical Physics

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The determination of phase behavior and, in particular, the nature of phase transitions in twodimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by use of the random sequential adsorption with surface diffusion (RSAD) model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage. arXiv:1908.05555v1 [cond-mat.soft]

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“…The configuration of the system can thus be fully specified by the spatial coordinates of the heads of all the cubes in the system. We study the model using grand canonical Monte Carlo simulations implementing an algorithm which includes cluster moves [45,56,57,62] that help in equilibrating systems of hard particles with large excluded volume at densities close to full packing [45,56] or at full packing [57]. Below, we briefly summarise the algorithm.…”

Section: Model and Algorithmmentioning

confidence: 99%

Phase diagram of a system of hard cubes on the cubic lattice

et al. 2019

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We study the phase diagram of a system of 2 × 2 × 2 hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size 2 × L × L where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solid-like sublattice ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size 2 × 2 × L where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters, which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the O(3) universality class perturbed by cubic anisotropy as predicted by the Landau theory.

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

Cited by 44 publications

References 97 publications

Different phases of a system of hard rods on three dimensional cubic lattice

Different phases of a system of hard rods on three dimensional cubic lattice

Liquid-hexatic-solid phase transition of a hard-core lattice gas with third neighbor exclusion

Phase diagram of a system of hard cubes on the cubic lattice

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