Some inequalities for correlation functions of Ising models with quenched randomness
Disordered Systems and Neural Networks
2020-04-14 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
Correlation inequalities have played an essential role in the analysis of ferromagnetic models but have not been established in spin glass models. In this study, we obtain some correlation inequalities for the Ising models with quenched randomness, where the distribution of the interactions is symmetric. The acquired inequalities can be regarded as an extension of the previous results, which were limited to the local energy for a spin set, to the local energy for a pair of spin sets. Besides, we also obtain some correlation inequalities for asymmetric distribution.
Keywords
Cite
@article{arxiv.2004.05832,
title = {Some inequalities for correlation functions of Ising models with quenched randomness},
author = {Manaka Okuyama and Masayuki Ohzeki},
journal= {arXiv preprint arXiv:2004.05832},
year = {2020}
}
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11 pages, 0 figure