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

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.

scholarly journals Percolation and the hard-core lattice gas model

1994 ◽  
Vol 49 (2) ◽  
pp. 179-197 ◽  
Author(s):  
J. van den Berg ◽  
J.E. Steif
Keyword(s):  
Lattice Gas ◽  
Hard Core ◽  
Lattice Gas Model

scholarly journals An Improvement of the Lovász Local Lemma via Cluster Expansion

2011 ◽  
Vol 20 (5) ◽  
pp. 709-719 ◽  
Author(s):  
RODRIGO BISSACOT ◽  
ROBERTO FERNÁNDEZ ◽  
ALDO PROCACCI ◽  
BENEDETTO SCOPPOLA
Keyword(s):  
Partition Function ◽  
Recent Result ◽  
Cluster Expansion ◽  
Lattice Gas ◽  
Hard Core ◽  
Independent Set ◽  
Lovász Local Lemma ◽  
Local Lemma ◽  
Lovasz Local Lemma

An old result by Shearer relates the Lovász local lemma with the independent set polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition function of the hard-core lattice gas on graphs. We use this connection and a recent result on the analyticity of the logarithm of the partition function of the abstract polymer gas to get an improved version of the Lovász local lemma. As an application we obtain tighter bounds on conditions for the existence of Latin transversal matrices.

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