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arXiv · 1003.2715

Spherical spin-glass - Coulomb gas duality: solution beyond mean-field theory

Shimul Akhanjee·Joseph Rudnick
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Abstract

We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé $τ^{IV} [n]$ function in the $n\to 0$ limit. The large $N$ thermodynamics exactly recovers that of Kosterlitz, Thouless and Jones \cite{ktjonesPRL}. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.

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Shimul Akhanjee, Joseph Rudnick. 2010-06-27. Spherical spin-glass - Coulomb gas duality: solution beyond mean-field theory. https://doi.org/10.1103/physrevlett.105.047206

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