Computation of the Zero Temperature RSB parameter in Bethe Lattice Spin Glasses

TL;DR

This paper numerically computes the zero-temperature RSB order parameter in Bethe Lattice Spin Glasses with finite connectivity, revealing the organization of states near the phase transition using a universal formula.

Contribution

It introduces a numerical method to calculate the zero-temperature RSB order parameter in BLSG based on a universal relation involving energy gap distributions.

Findings

Order parameter computed near the transition point.

Distribution of energy gaps derived numerically.

Method applicable to finite connectivity spin glasses.

Abstract

Bethe Lattice Spin Glasses (BLSG) are models with finite connectivity which undergo a Replica Symmetry Breaking (RSB) phase transition in field, even at zero temperature. The order parameter describing this phase is a function related to the non-trivial organization of the states. We compute numerically the spin glass order parameter at zero temperature in BLSG with coordination number $z=3$ and couplings $J=\pm1$, near the transition. The method is based on a universal formula which relates the order parameter to the joint probability distribution of the energy gaps of the lowest lying states. Such distribution is derived numerically by introducing a convenient bulk perturbation to the Hamiltonian.