Time Dependent Local Field Distribution and Metastable States in the SK-Spin-Glass

TL;DR

This paper investigates the time-dependent local field distribution and metastable states in the SK spin glass model at zero temperature, comparing dynamic methods with replica symmetry breaking theory, revealing differences in energy states and local field distributions.

Contribution

It introduces a detailed analysis of metastable states and local field distributions in the SK model using Monte Carlo and Fokker-Planck approaches, contrasting dynamic results with replica theory.

Findings

Dynamic energies are higher than the replica ground state energy.

Tapping and simulated annealing produce energies close to the ground state.

Local field distribution tends to zero for small fields, contrasting with Edwards hypothesis.

Abstract

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A comparison with replica symmetry broken theory, evaluated in high orders, shows that the energies obtained via dynamics are higher than the ground state energy of replica theory. Tapping and simulated annealing yield on the other hand results which are very close to the ground state energy. The local field distribution tends to zero for small fields. This is in contrast to the Edwards flat measure hypothesis. The distribution of energies obtained for different tapping strengths does again not follow the canonical form proposed by Edwards.