Numerical Evidence for Continuity of Mean Field and Finite Dimensional Spin Glasses

Abstract

We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the full $P(q)$ are smooth, and do not show any discontinuity. Different lattice sizes are used to provide evidence for a smooth behavior of disorder averages in the thermodynamic limit. Quantities defined on a given realization of the disorder show a chaotic behavior. Our results support the validity of a Replica Symmetry Breaking description of finite dimensional models.

4 pages, ps color figures

References in corpus (3)

• About the overlap distribution in mean field spin glass models
• Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
• Numerical Simulations of Spin Glass Systems

Cited by in corpus (4)

• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• The nature of ergodicity breaking in Ising spin glasses as revealed by correlation function spectral properties
• Evidence for the double degeneracy of the ground-state in the 3D $\pm J$ spin glass