A cluster model of critical dynamics

Z. Alexandrowicz

Physica A: Statistical Mechanics and its Applications, 1993, vol. 194, issue 1, 154-162

Abstract: Critical relaxation (exponent z) is described by a reversible growth of clusters: Particles of a cluster are ordered into connected sequences, such that a stepwise variation of their length describes relaxation. We derive z = z(ϱ, β, ν) where ϱ is a scaling exponent relating cluster size to connected length at equilibrium, available from simulation of Ising clusters. Furthermore, a Flory-like equation gives ϱ = ϱ(β, ν), and hence z = z(ϱ, ν). In D = 2 and 3, theoretical z(β, ν) an simulation-aided z(ϱ, β, ν) agree reasonably well with each other and with direct simulations of z. In D = 4 - ε, z(β, ν) agrees with the exact RG.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:194:y:1993:i:1:p:154-162

DOI: 10.1016/0378-4371(93)90349-9

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