scholarly journals Husimi-lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Nathann T. Rodrigues ◽  
Tiago J. Oliveira
Keyword(s):  
Lattice Gases ◽  
Square Lattice ◽  
Husimi Lattice ◽  
Method Analysis

Theoretical Models of Cooperative Dynamics Near the Glass Transition

1990 ◽  
Vol 215 ◽  
Author(s):  
Josef Jäckle
Keyword(s):  
Glass Transition ◽  
Lattice Gas ◽  
Finite Size ◽  
Theoretical Models ◽  
Lattice Gases ◽  
Bootstrap Percolation ◽  
Square Lattice ◽  
High Particle Concentration ◽  
High Particle ◽  
Percolation Problem

AbstractIt is shown that diffusion in the hard-square and hard-octahedron lattice gases at high particle concentration has cooperative properties resembling molecular relaxation in undercooled liquids near the glass transition. For these models a characteristic length of cooperativity is introduced by an underlying percolation problem, which determines whether permanently blocked particles exist in lattices of finite size. The percolation problem belongs to a general class of bootstrap percolation models. Salient Monte Carlo results for the concentration and size dependence of self diffusion in the hard-square lattice gas are presented. Similarities with the n-spin facilitated kinetic Ising models are also pointed out.

INTERFACE INSTABILITY IN DRIVEN LATTICE GASES

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 954-958 ◽  
Author(s):  
G. SZABÓ ◽  
A. SZOLNOKI ◽  
T. ANTAL ◽  
I. BORSOS
Keyword(s):  
Lattice Gas ◽  
Nearest Neighbor ◽  
Interfacial Instability ◽  
Lattice Gases ◽  
Square Lattice ◽  
Wave Number ◽  
Material Transport ◽  
Interface Instability ◽  
Amplification Rate ◽  
Lattice Gas Models

In driven lattice-gas models, the enhanced material transport along the interfaces results in an instability of the planar interfaces and leads to the formation of multistrip states. To study the interfacial instability, Monte Carlo simulations are performed on different square lattice-gas models. The amplification rate of a periodic perturbation depends on the wave number k; it has a positive maximum at a characteristic value of k on the analogy of the Mullins-Sekerka instability. Significant differences have been found in the dependence of amplification rate on k when comparing the systems with nearest neighbor repulsive and nearest and next-nearest neighbor attractive interactions. The results agree qualitatively with theories neglecting the fluctuations.

MANY-DIMENSIONAL LORENTZ CELLULAR AUTOMATA AND TURING MACHINES

1996 ◽  
Vol 06 (06) ◽  
pp. 1127-1135 ◽  
Author(s):  
LEONID A. BUNIMOVICH
Keyword(s):  
Cellular Automata ◽  
Artificial Life ◽  
Lattice Gases ◽  
Square Lattice ◽  
Turing Machines ◽  
Natural Conditions ◽  
Vortex Sheets ◽  
Cubic Lattices ◽  
Higher Dimensional ◽  
Lorentz Lattice Gases

We study the class of cellular automata that generalizes the Lorentz lattice gases in statistical mechanics, the models of industrious ants in the theory of an artificial life and the so-called Tur-mites (many-dimensional Turing machines). We prove that on the square lattice ℤd, d = 2, the existence of a bounded orbit of a particle (ant, machine) determines all nondegenerate local scattering rules (states of a machine). For higher dimensional (d ≥ 3) cubic lattices we show that under some natural conditions all possible bounded orbits (vortices) can live only in some “vortex sheets” that have a dimension strictly less than d.

scholarly journals Phase transitions of antiferromagnetic Ising spins on the zigzag surface of an asymmetrical Husimi lattice

2019 ◽  
Vol 6 (3) ◽  
pp. 181500 ◽  
Author(s):  
Ran Huang ◽  
Purushottam D. Gujrati
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Spontaneous Magnetization ◽  
Square Lattice ◽  
Two Dimensional ◽  
Simple Formulation ◽  
First Order ◽  
Husimi Lattice ◽  
Antiferromagnetic Ising Model ◽  
Ising Spins

An asymmetrical two-dimensional Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice, which we have previously applied to study polymers near a surface. The model retains the advantages of simple formulation and exact calculation of the conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on the surface of this lattice to evaluate thermal properties such as free energy, energy density and entropy, from which we have successfully identified a first-order order–disorder transition other than the spontaneous magnetization, and a secondary transition on the supercooled state indicated by the Kauzmann paradox.

scholarly journals Equation of state for hard-square lattice gases

2007 ◽  
Vol 75 (5) ◽  
Author(s):  
Heitor C. Marques Fernandes ◽  
Yan Levin ◽  
Jeferson J. Arenzon
Keyword(s):  
Equation Of State ◽  
Lattice Gases ◽  
Square Lattice
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