Free-Energy Barriers in Spin Glasses from Multi-Overlap Simulations 1

Abstract

We present, results of recent, high statistics Monte Carlo studies of the Edwards-Anderson Ising spin-glass model in three and four dimensions. The simulations are based on a non-Boltzmann sampling technique, the multi-overlap algorithm which will be briefly reviewed. Physically we mainly discuss those properties of the probability density ${\mathit{P}}_{\mathcal{J}}\mathrm{(}\mathit{q}\mathrm{)}$ of the Parisi overlap parameter q which are difficult, to obtain with standard canonical Boltzmann sampling. In particular we focus on the free-energy barriers ${\mathit{F}}_{\mathit{B}}^{\mathit{q}}$ which are visible in ${\mathit{P}}_{\mathcal{J}}\mathrm{(}\mathit{q}\mathrm{)}$ and the behavior of the tails of the averaged probability density.