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Conductivity of Coniglio-Klein clusters.
MedLine Citation:
PMID:  23214771     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
We performed numerical simulations of the q-state Potts model to compute the reduced conductivity exponent t/ν for the critical Coniglio-Klein clusters in two dimensions, for values of q in the range [1,4]. At criticality, at least for q<4, the conductivity scales as C(L)∼L^{-t/ν}, where t and ν are, respectively, the conductivity and correlation length exponents. For q=1, 2, 3, and 4, we followed two independent procedures to estimate t/ν. First, we computed directly the conductivity at criticality and obtained t/ν from the size dependence. Second, using the relation between conductivity and transport properties, we obtained t/ν from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated t/ν to be 0.986±0.012, 0.877±0.014, 0.785±0.015, and 0.658±0.030, for q=1, 2, 3, and 4, respectively. We also evaluated t/ν for noninteger values of q and propose the conjecture 40gt/ν=72+20g-3g^{2} for the dependence of the reduced conductivity exponent on q, in the range 0⩽q⩽4, where g is the Coulomb gas coupling.
Authors:
Nicolas Posé; N A M Araújo; H J Herrmann
Publication Detail:
Type:  Journal Article     Date:  2012-11-30
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  86     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2012 Nov 
Date Detail:
Created Date:  2012-12-11     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  051140     Citation Subset:  IM    
Affiliation:
Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, CH-8093 Zurich, Switzerland.
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