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Fortuin-Kasteleyn and damage-spreading transitions in random-bond Ising lattices

P. H. Lundow¹ and I. A. Campbell²

¹Department of Theoretical Physics, Kungliga Tekniska högskolan, SE-106 91 Stockholm, Sweden
²Laboratoire Charles Coulomb, Université Montpellier II, 34095 Montpellier, France

Phys. Rev. E 86, 041121 – Published 12 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041121

Abstract

The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures $T_{FK} (p)$ and $T_{DS} (p)$ are studied on random-bond Ising models of dimensions 2–5 and as functions of the ferromagnetic interaction probability $p$ ; the conjecture that $T_{DS} (p) \sim T_{FK} (p)$ is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn $T_{FK} (p)$ transition line and the Nishimori line $[p_{NL,FK}, T_{NL,FK}]$ . There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration $[p_{NL,FK}]$ , the damage spreading $T_{DS} (p)$ is found to be equal to $T_{FK} (p)$ to within $0.1 %$ . For the other dimensions, however, $T_{DS} (p)$ is observed to be systematically a few percent lower than $T_{FK} (p)$ .

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