Spin glass to paramagnetic transition and triple point in Spherical SK model
Abstract
This paper studies spin glass to paramagnetic transition in the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant and inverse temperature . The disorder of the system is represented by a general Wigner matrix. We confirm a conjecture of \cite{Baik2016} and \cite{Baik2017}, that the critical window of temperatures for this transition is with . The limiting distribution of the scaled free energy is Gaussian for negative and a weighted linear combination of independent Gaussian and Tracy-Widom components for positive . In the special case where the Wigner matrix is from the Gaussian Orthogonal or Unitary Ensemble, we describe the triple point transition between spin glass, paramagnetic, and ferromagnetic regimes in a critical window for around the triple point : the Tracy-Widom component is replaced by the one parameter family of deformations described by Bloemendal and Virag, \cite{BloVirI}.
Keywords
Cite
@article{arxiv.2104.07629,
title = {Spin glass to paramagnetic transition and triple point in Spherical SK model},
author = {Iain M. Johnstone and Yegor Klochkov and Alexei Onatski and Damian Pavlyshyn},
journal= {arXiv preprint arXiv:2104.07629},
year = {2024}
}
Comments
Submitted version of paper to appear in J. Stat. Phys