Inequality for local energy of Ising models with quenched randomness and its application

Manaka Okuyama, Masayuki Ohzeki

Published 2020-01-29Version 1

We extend a lower bound on average of local energy for the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] to asymmetric distribution. Compared to the case of symmetric distribution, our bound has a non-trivial term. Applying the attained bound to the Gaussian distribution, we obtain lower bounds on the expected value of the square of the correlation function. As a result, we show that, in the Ising model with the Gaussian random field, the spin-glass order parameter always has a finite value at any temperature, regardless of the form of other interactions.