The Fortuin-Kasteleyn and Damage Spreading transitions in Random bond Ising lattices

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 dimension two to five and as functions of the ferromagnetic interaction probability p; the conjecture that T_{ds}(p) ~ 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 three, 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).

10 pages, 12 figures

References in corpus (12)

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• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
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• Simplest model to study reentrance in physical systems
• Spreading with immunization in high dimensions
• Distribution of Lee-Yang zeros and Griffiths singularities in the $\pm J$ model of spin glasses
• Renormalization group approach to exact sampling
• Damage spreading and coupling in Markov chains
• Convergence and coupling for spin glasses and hard spheres
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Cited by in corpus (6)

• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• Spin glasses and percolation
• Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• Damage Spreading in a Driven Lattice Gas Model
• Damage spreading in the random cluster model