Explicit generation of the branching tree of states in spin glasses

TL;DR

This paper introduces a numerical method to explicitly generate the tree of states in mean-field spin glasses, providing insights into the spin-glass phase structure and enabling detailed analysis of physical observables.

Contribution

The authors develop a cavity-based numerical approach to explicitly construct the state tree in spin glasses, enhancing understanding of replica symmetry breaking.

Findings

Illuminates the physical meaning of full replica symmetry breaking

Enables evaluation of complex observables like correlation functions

Analyzes finite-size effects in overlap distributions

Abstract

We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed information on the structure of the spin-glass phase. A cavity approach ensures that the method is self-consistent and permits the evaluation of sophisticated observables, such as correlation functions. We include an example application to the study of finite-size effects in single-sample overlap probability distributions, a topic that has attracted considerable interest recently.