The SK model is infinite step replica symmetry breaking at zero temperature
Probability
2021-06-18 v2 Mathematical Physics
math.MP
Abstract
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.
Keywords
Cite
@article{arxiv.1703.06872,
title = {The SK model is infinite step replica symmetry breaking at zero temperature},
author = {Antonio Auffinger and Wei-Kuo Chen and Qiang Zeng},
journal= {arXiv preprint arXiv:1703.06872},
year = {2021}
}
Comments
revised version; 20 pages