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arXiv · 1412.1909

Replica analysis of Franz-Parisi potential for sparse systems

Masahiko Ueda·Yoshiyuki Kabashima
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Abstract

We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the characteristic structure of multi-body overlaps, and the self-consistent equations under this solution are equivalent to the one-step replica symmetry breaking (1RSB) cavity equation with Parisi parameter $x=1$. This method is useful for the evaluation of transition temperatures of the $p$-spin model on regular random graphs under a uniform magnetic field.

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Masahiko Ueda, Yoshiyuki Kabashima. 2014-12-05. Replica analysis of Franz-Parisi potential for sparse systems. https://doi.org/10.1088/1751-8113/48/13/135002

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