Local Spin Glass Order in 1D
Silvio Franz, Giorgio Parisi
TL;DR
This paper investigates how one-dimensional Kac spin glasses transition from local mean field behavior to global paramagnetism as the interaction range varies, using Monte Carlo simulations to analyze correlation growth.
Contribution
It provides a detailed numerical analysis of correlation growth and phase behavior in 1D Kac spin glasses, especially near the mean-field critical region.
Findings
Correlations grow faster than the interaction range in the low temperature phase.
A crossover from local mean field to paramagnetism is observed.
Correlation growth near the critical region is fully characterized.
Abstract
We study the behavior of one dimensional Kac spin glasses as function of the interaction range. We verify by Montecarlo numerical simulations the crossover from local mean field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region.
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