Phase transitions in the multicomponent Widom-Rowlinson model and in hard cubes on the bcc lattice

Nielaba, Peter; Lebowitz, Joel L.

doi:10.1016/s0378-4371(97)00245-8

Cited by 7 publications

(6 citation statements)

References 20 publications

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“…One observes the value p * ≈ 0.75 for all cases after which the relative frequency of the dominant species becomes ≈ 1. It is interesting to observe that while all four examples show a phase transition just below p * ≈ 0.75, the configuration of Figure 2(a) provides evidence for an intermediate phase with a second transition at a lower value of p. Note that in this case we have total symmetry between the four species and the result is qualitatively consistent with the case of equal EDs [8].…”

Section: A Spin-flip Process For Simulating the Lattice Wr-modelsupporting

confidence: 66%

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Dominance of most tolerant species in multi-type lattice Widom–Rowlinson models

Mazel¹,

Suhov

Stuhl

et al. 2014

J. Stat. Mech.

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We analyse equilibrium phases in a multi-type lattice Widom-Rowlinson model with (i) four particle types, (ii) varying exclusion diameters between different particle types and (iii) large values of fugacity. Contrary to an expectation, it is not the most "aggressive" species, with largest diameters, which dominates the equilibrium measure, but the "most tolerant" one, which has smallest exclusion diameters. Results of numerical simulations are presented, showing densities of species in equilibrium phases and confirming the theoretical picture.

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Section: A Spin-flip Process For Simulating the Lattice Wr-modelsupporting

confidence: 66%

“…Aspects of these models have been studied e.g. in [3,4,5,6,7,8,9] (see also the bibliography therein). In the case of a multitype model it was assumed that different particles have the same EDs.…”

Section: Introductionmentioning

confidence: 99%

Dominance of most tolerant species in multi-type lattice Widom–Rowlinson models

Mazel¹,

Suhov

Stuhl

et al. 2014

J. Stat. Mech.

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“…Results on scaling behavior [19] support an Ising-like critical point, as expected on grounds of symmetry. Subsequent studies of the WRLG have focussed on multi-species versions [22]. Here we study the driven WRLG: as in the KLS model, and the driven NNE lattice gas, particle motion is favored along one direction, and suppressed in the opposite sense, as if an electric or other external field were acting on the particles.…”

Section: Introductionmentioning

confidence: 98%

Driven Widom-Rowlinson lattice gas

Dickman

Zia

2018

Phys. Rev. E

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In the Widom-Rowlinson lattice gas, two particle species (A, B) diffuse freely via particle-hole exchange, subject to both on-site exclusion and prohibition of A-B nearest-neighbor pairs. As an athermal system, the overall densities are the only control parameters. As the densities increase, an entropically driven phase transition occurs, leading to ordered states with A- and B-rich domains separated by hole-rich interfaces. Using Monte Carlo simulations, we analyze the effect of imposing a drive on this system, biasing particle moves along one direction. Our study parallels that for a driven Ising lattice gas, the Katz-Lebowitz-Spohn (KLS) model, which displays atypical collective behavior, e.g., structure factors with discontinuity singularities and ordered states with domains only parallel to the drive. Here, other interesting features emerge, including structure factors with kink singularities (best fitted to |q|), maxima at nonvanishing wave-vector values, oscillating correlation functions, and ordering into multiple striped domains perpendicular to the drive, with a preferred wavelength depending on density and drive intensity. Moreover, the (hole-rich) interfaces between the domains are statistically rough (whether driven or not), in sharp contrast with those in the KLS model, in which the drive suppresses interfacial roughness. Defining an order parameter that accounts for the emergence of multistripe states, we map out the phase diagram in the density-drive plane and present preliminary evidence for a critical phase in this driven lattice gas.

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“…proving property (b). Substituting (14) into identity (13) and using (12), we deduce that every y, z ∈ X s with y = z and for every t ≥ 0,…”

Section: Analysis Of the Energy Landscapementioning

confidence: 99%

“…The multicomponent Widom-Rowlison model has been studied also in the continuum and with many of the variants described above for the case M = 2, see e.g. [5,8,9,14,16].…”

Section: Introductionmentioning

confidence: 99%

Low-Temperature Behavior of the Multicomponent Widom–Rowlison Model on Finite Square Lattices

Zocca

2018

J Stat Phys

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We consider the multicomponent Widom-Rowlison with Metropolis dynamics, which describes the evolution of a particle system where M different types of particles interact subject to certain hard-core constraints. Focusing on the scenario where the spatial structure is modeled by finite square lattices, we study the asymptotic behavior of this interacting particle system in the low-temperature regime, analyzing the tunneling times between its M maximum-occupancy configurations, and the mixing time of the corresponding Markov chain. In particular, we develop a novel combinatorial method that, exploiting geometrical properties of the Widom-Rowlinson configurations on finite square lattices, leads to the identification of the timescale at which transitions between maximum-occupancy configurations occur and shows how this depends on the chosen boundary conditions and the square lattice dimensions.corresponding to the energy landscape (X , H, q) where the state space X is given in (2) and the energy H and connectivity function q are chosen as follows.The energy function or Hamiltonian H : X → R counts the number of particles, regardless of their type:

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Phase transitions in the multicomponent Widom-Rowlinson model and in hard cubes on the bcc lattice

Cited by 7 publications

References 20 publications

Dominance of most tolerant species in multi-type lattice Widom–Rowlinson models

Dominance of most tolerant species in multi-type lattice Widom–Rowlinson models

Driven Widom-Rowlinson lattice gas

Low-Temperature Behavior of the Multicomponent Widom–Rowlison Model on Finite Square Lattices

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