Inequality for local energy of Ising models with quenched randomness and its application
arXiv:2001.10707 · doi:10.7566/JPSJ.89.064704
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.
arXiv comment6 pages, 0 figure, to appear in J. Phys. Soc. Jpn
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