Numerical Evidence for Spontaneously Broken Replica Symmetry in 3D Spin

 Glasses

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Abstract

By numerical simulations of the \(3d\) Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.

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Infinite Number of Order Parameters for Spin-Glasses

G Parisi (1979)

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Simulated Tempering: A New Monte Carlo Scheme

Giorgio Parisi, Enzo Marinari (1992)

We propose a new global optimization method ({\em Simulated Tempering}) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyze and discuss the conditions under which the method has optimal performances.