Using memory to identify phase transitions on a Cayley Tree

Auditya Sharma; Javier M. Magan

Using memory to identify phase transitions on a Cayley Tree

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arxiv 1304.7008 v2 pith:3MYA66B2 submitted 2013-04-25 cond-mat.stat-mech gr-qc

Javier M. Magan , Auditya Sharma This is my paper

classification cond-mat.stat-mechgr-qc

keywords memoryphasetransitioncarlocayleyclearmontesignal

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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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