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 detailed examination and state-of-the-art simulation provide a coherent picture of many pure states, explain the previous findings, and the controversy is solved. The pertinent status of the number of pure states beyond this statistic is also discussed, and we find the spin glass balance is overall tilting towards many pure states studied by simulations.