Using memory to identify phase transitions on a Cayley Tree

2013/04/25 by Javier M. Magán, Magan, Javier M., Auditya Sharma +1
Computer Science · #Evolutionary Algorithms and Applications #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1304.7008

openalex publication_date 2013/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a concrete and systematic connection between the statistical physics of the Ising ferromagnet on a Cayley tree, and the study of memory in exponentially expanding spaces. Memory turns out to be a clear signal of the `Bethe-Peierls' phase transition, and the average of memory divided by its standard deviation provides a clear signal of the `spin-glass' transition temperature. Numerical Monte Carlo simulations are used to make transparent the existence of the two different transition temperatures. The quantities used to spot the phase transitions with Monte Carlo could be useful when studying other systems where analytical methods don't work.

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