High-dimensional Gaussian fields with isotropic increments seen through spin glasses

Abstract

We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle-point variational representation in terms of a Parisi-type functional for the free energy in the infinite-dimensional limit. The proofs are based on the techniques developed in the course of the rigorous analysis of the Sherrington-Kirkpatrick model with vector spins.

13 pages

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Classical Particle in a Box with Random Potential: exploiting rotational symmetry of replicated Hamiltonian
• Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite dimensional Euclidean spaces
• Free energy in the generalized Sherrington-Kirkpatrick mean field model

Cited by in corpus (1)

• Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution