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arXiv · 1610.03941

Replica Symmetry Breaking without Replicas

Simone Franchini
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Abstract

We introduce a mathematical framework based on simple combinatorial arguments (Kernel Representation) that allows to deal successfully with spin glass problems, among others. Let $Ω^{N}$ be the space of configurations of an $N-$ spins system, each spin having a finite set $Ω$ of inner states, and let $μ:Ω^{N}\rightarrow\left[0,1\right]$ be some probability measure. Here we give an argument to encode $μ$ into a kernel function $M:\left[0,1\right]^{2}\rightarrowΩ$, and use this notion to reinterpret the assumptions of the Replica Symmetry Breaking ansatz (RSB) of Parisi et Al. [1, 2], without using replicas, nor averaging on the disorder.

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Simone Franchini. 2023-01-10. Replica Symmetry Breaking without Replicas. https://doi.org/10.1016/j.aop.2023.169220

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