arXiv subjects

Chokri Manai

Publications and source records attributed to Chokri Manai.

20 records · Page 2Linked to original sources

arXiv2019

The Quantum Random Energy Model as a Limit of p-Spin Interactions

We consider the free energy of a mean-field quantum spin glass described by a $ p $-spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \infty $, i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the $ p $-spin model converges in a joint thermodynamic and $ p \to \infty $ limit to the free energy of the QREM.

math-ph↗

arXiv2019

Phase Diagram of the Quantum Random Energy Model

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.

math-ph↗