Hopping conductivity in the extended hard-core square lattice gas

1990 ◽  
Vol 41 (10) ◽  
pp. 7156-7161 ◽  
Author(s):  
Radu Pitiş
Keyword(s):  
Lattice Gas ◽  
Hard Core ◽  
Square Lattice ◽  
Hopping Conductivity

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

The Equation of State for a one-component System

1974 ◽  
Vol 29 (1) ◽  
pp. 65-74 ◽  
Author(s):  
H. P. Neumann
Keyword(s):  
Long Range ◽  
Lattice Gas ◽  
Particle Interaction ◽  
Hard Core ◽  
State Diagram ◽  
Phase Changes ◽  
Square Lattice ◽  
Temperature Phase ◽  
Density State ◽  
Transcendental Equations

The cooperative problem for a lattice gas on a plane, square lattice and on a simple cubic lattice is solved by a system of two coupled, transcendental equations, derived by a combinatorial method, which describes a homogeneous or periodical particle density on the lattice as a function of the temperature and the chemical potential of the lattice-gas.For the particle interaction a Hard-Core potential (nearest neighbour exclusion) with a soft long-range tail is assumed. The zero-component of the Fourier-transform of this long-range interaction part can be positive or negative. The system of transcendental equations is solved by a graphic method. As a result, the complete pressure-density state diagram and the pressure-temperature phase diagram can be drawn. The lattice-gas exists in three stable phases: gas, liquid and solid. Three phase changes are possible: condensation, crystallization and sublimation. Critical points of condensation and freezing are examined. The number of possible phases and phase changes at a fixed temperature depends on the geometric structure of the particle interaction.

Hard-square lattice gas

1980 ◽  
Vol 22 (4) ◽  
pp. 465-489 ◽  
Author(s):  
R. J. Baxter ◽  
I. G. Enting ◽  
S. K. Tsang
Keyword(s):  
Lattice Gas ◽  
Square Lattice

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.

scholarly journals Fluctuations and correlations of a driven tracer in a hard-core lattice gas

2013 ◽  
Vol 87 (3) ◽  
Author(s):  
O. Bénichou ◽  
P. Illien ◽  
G. Oshanin ◽  
R. Voituriez
Keyword(s):  
Lattice Gas ◽  
Hard Core
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