Phase Diagram of the Quantum Random Energy Model
Mathematical Physics
2020-02-19 v1 math.MP
Abstract
We prove Goldschmidt's formula [Phys. Rev. B 47 (1990) 4858] for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is based on a combination of variational methods on the one hand, and percolation bounds on large-deviation configurations in combination with simple spectral bounds on the hypercube's adjacency matrix on the other hand.
Keywords
Cite
@article{arxiv.1909.07180,
title = {Phase Diagram of the Quantum Random Energy Model},
author = {Chokri Manai and Simone Warzel},
journal= {arXiv preprint arXiv:1909.07180},
year = {2020}
}
Comments
12 pages, 1 figure