Energy barriers in SK spin-glass model

Abstract

The height of barriers separating metastable states is studied for the infinite range Ising spin-glass model. A barrier configuration corresponds to a saddle point {mi, i = 1, ..., N, — 1 ≤ mi ≤ 1} of an energy surface that smoothly interpolates the energy in the hypercube. For low energy barriers, which are relevant for the dynamics, the number of independent descending directions from the saddle point is finite when N → ∞. It is found that these descending directions are contained in the linear subspace of the hypercube [—1,1]N generated by directions for which Σ j Jij mj = 0. Numerical estimates were performed by two distinct algorithms which lead to consistent results. Assuming barrier heights growing with system size N as Nα we find α = 0.34 ± 0.08