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arXiv · 1101.3658

Replica analysis of partition-function zeros in spin-glass models

Kazutaka Takahashi
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Abstract

We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.

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Kazutaka Takahashi. 2011-01-19. Replica analysis of partition-function zeros in spin-glass models. https://doi.org/10.1088/1751-8113/44/23/235001

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