Inequality for local energy of Ising models with quenched randomness and its application
Disordered Systems and Neural Networks
2020-05-14 v3 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
In this study, we extend the lower bound on the average of the local energy of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] obtained for a symmetric distribution to an asymmetric one. Compared with the case of symmetric distribution, our bound has a non-trivial term. By applying the acquired bound to a Gaussian distribution, we obtain the lower bounds on the expectation of the square of the correlation function. Thus, we demonstrate that in the Ising model in a Gaussian random field, the spin-glass order parameter generally has a finite value at any temperature, regardless of the forms of the other interactions.
Cite
@article{arxiv.2001.10707,
title = {Inequality for local energy of Ising models with quenched randomness and its application},
author = {Manaka Okuyama and Masayuki Ohzeki},
journal= {arXiv preprint arXiv:2001.10707},
year = {2020}
}
Comments
6 pages, 0 figure, to appear in J. Phys. Soc. Jpn