Universality inp-spin glasses with correlated disorder

Valentin Bonzom, Razvan Gurau, Matteo Smerlak
2013 Journal of Statistical Mechanics: Theory and Experiment  
We introduce a new method, based on the recently developed random tensor theory, to study the p-spin glass model with non-Gaussian, correlated disorder. Using a suitable generalization of Gurau's theorem on the universality of the large N limit of the p-unitary ensemble of random tensors, we exhibit an infinite family of such non-Gaussian distributions which leads to same low temperature phase as the Gaussian distribution. While this result is easy to show (and well known) for uncorrelated
more » ... r uncorrelated disorder, its robustness with respect to strong quenched correlations is surprising. We show in detail how the critical temperature is renormalized by these correlations. We close with a speculation on possible applications of random tensor theory to finite-range spin glass models.
doi:10.1088/1742-5468/2013/02/l02003 fatcat:5wwmk2pyfrhkxgppc37dux5ffu