Random Energy Model as a paradigm of complex systems

TL;DR

This paper explores the Random Energy Model (REM) as a fundamental framework for understanding complex systems, highlighting its relation to physical phenomena like spin glasses and phase transitions.

Contribution

It extends REM to quadratic cases and identifies key features like hierarchical free energies and symmetry loss, linking REM to diverse complex phenomena.

Findings

Identification of double thermodynamic reflection in REM

Connection of REM to spin glass and ferromagnetic phases

Analysis of physical phenomena through REM framework

Abstract

A quadratic extension of REM has been treated. Discussed here is the origin of relation of REM to strings and other complex physical phenomena. Two basic features of the REM class of complex phenomena were identified: the double thermodynamic reflection (a hierarchy of free energies) including the strong reflection at the upper level (the free energy on the order of a logarithm of the degrees of freedom) and the loss (complete or partial) of the local symmetry property. Two main classes of complex phenomena related to REM are seen: the spin glass phase of REM and the boundary the spin glass-ferromagnetic phases. Some examples of physics interest are analyzed from this viewpoint.