Quantifying Errors in Effective Cluster Interactions of Lattice Gas Cluster Expansions

2022 ◽  
Author(s):  
Greg Collinge ◽  
Alyssa Hensley ◽  
Jean-Sabin McEwen
Keyword(s):  
Lattice Gas ◽  
Cluster Expansions ◽  
Effective Cluster

Modified Fisher Droplet Model

1982 ◽  
Vol 21 ◽  
Author(s):  
J. Marro ◽  
R. Toral
Keyword(s):  
Cluster Size ◽  
Lattice Gas ◽  
Three Dimensional ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Exact Results ◽  
Droplet Model ◽  
Simple Modification ◽  
The Magnetic Field ◽  
Effective Cluster

ABSTRACTWe propose a simple modification of the Fisher droplet model which, unlike classical nucleation theory, reproduces very well some Monte Carlo equilibrium cluster distributions P1 for the three-dimensional Ising or lattice gas model. It then follows that p1(h) /p1(h=0) = A exp(− η l) where η ∝hl/Y, y≃0.45, when the magnetic field h is small enough, as suggested from the consideration of an effective cluster size ly , while η seems rather proportional to h at larger values of the field, as implied by some exact results.

Critical phenomena in a binary lattice gas. I. Cluster expansions and transcriptions

1979 ◽  
Vol 20 (5) ◽  
pp. 2014-2033 ◽  
Author(s):  
John C. Wheeler ◽  
J. Anthony Gualtieri
Keyword(s):  
Critical Phenomena ◽  
Lattice Gas ◽  
Cluster Expansions ◽  
Binary Lattice

HOPPING AND STATIC CORRELATIONS OF HIGHER ORDER IN A LATTICE GAS

1985 ◽  
Vol 46 (C9) ◽  
pp. C9-141-C9-143 ◽  
Author(s):  
K. Froböse ◽  
J. Jäckle
Keyword(s):  
Lattice Gas ◽  
Higher Order

Counting Lattice-Gas Invariants

1993 ◽  
Author(s):  
Jeffrey Yepez
Keyword(s):  
Lattice Gas

scholarly journals Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

2020 ◽  
Vol 75 (5) ◽  
pp. 449-463
Author(s):  
Dominik Lips ◽  
Artem Ryabov ◽  
Philipp Maass
Keyword(s):  
Current Density ◽  
Lattice Gas ◽  
Yukawa Potential ◽  
Exclusion Process ◽  
Quantum Spin ◽  
Nonequilibrium Steady States ◽  
Interacting Particles ◽  
Driven Diffusive Systems ◽  
Periodic Potentials ◽  
Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

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