Non-differentiability of the effective potential and the replica symmetry breaking in the random energy model

Abstract

The effective potential for the two-replica system of the random energy model is exactly derived. It is an analytic function of the magnetizations of two replicas, ${\phi }^1$ and ${\phi }^2$ in the high-temperature phase. In the low-temperature phase, where the replica symmetry breaking takes place, the effective potential becomes non-analytic when ${\phi }^1={\phi }^2$. The non-analyticity is considered as a consequence of the condensation of the Boltzmann measure, which is a typical property of a glass phase.

15 pages, 6 figures; typos added, revised argument in section 2, results unchanged

References in corpus (4)

• The large deviation approach to statistical mechanics
• Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
• Are Bosonic Replicas Faulty?
• Exact replica treatment of non-Hermitean complex random matrices

Cited by in corpus (4)

• Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder
• Self-averaging of perturbation Hamiltonian density in perturbed spin systems
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Griffiths-type theorems for short-range spin glass models