The cavity method at zero temperature

TL;DR

This paper details the application of the cavity method at zero temperature to analyze the ground state energy and state complexity of a spin glass on a Bethe lattice with connectivity three, using one step replica symmetry breaking.

Contribution

It introduces a zero-temperature cavity method formalism for spin glasses on Bethe lattices, providing explicit calculations for ground state energy and state complexity.

Findings

Computed the ground state energy for a Bethe lattice with connectivity three.

Derived the complexity of equilibrium states at various energies.

Presented full results for the specific case of connectivity three.

Abstract

In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a Bethe lattice. The computation is done explicitly in the formalism equivalent to 'one step replica symmetry breaking'; we compute the energy of the global ground state, as well as the complexity of equilibrium states at a given energy. Full results are presented for a Bethe lattice with connectivity equal to three.