Using memory to identify phase transitions on a Cayley Tree
Statistical Mechanics
2013-11-20 v2 General Relativity and Quantum Cosmology
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.
Keywords
Cite
@article{arxiv.1304.7008,
title = {Using memory to identify phase transitions on a Cayley Tree},
author = {Javier M. Magan and Auditya Sharma},
journal= {arXiv preprint arXiv:1304.7008},
year = {2013}
}