Evidence of many thermodynamic states of the three-dimensional Ising spin glass

Abstract

We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure states regarding a controversial statistic, characterizing the fraction of centrally peaked disorder instances, of the overlap function order parameter. We observe that this statistic is subtly and sensitively influenced by the slight fluctuations of the integrated central weight of the disorder-averaged overlap function, making the asymptotic growth behaviour very difficult to identify. Modified statistics effectively reducing this correlation are studied and essentially monotonic growth trends are obtained. The effect of temperature is also studied, finding a larger growth rate at a higher temperature. Our state-of-the-art simulation and variance reduction data analysis suggest that the many pure state picture is most likely and coherent.

8 pages, 5 figures

References in corpus (8)

• Fractal free energy landscapes in structural glasses
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model
• Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions
• Some considerations of finite dimensional spin glasses
• Mean-value identities as an opportunity for Monte Carlo error reduction
• Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

Cited by in corpus (3)

• Multidimensional hyperspin machine
• Spin-glass dynamics: experiment, theory and simulation
• Uniqueness of ground state in the Edwards-Anderson spin glass model