Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls

The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the overlap distributions of periodic and free boundary conditions using population annealing Monte Carlo. For system sizes up to about 1000 spins, spin glasses show non-trivial spin overlap distributions. Periodic boundary conditions can trap diffusive domain walls which can contribute to small spin overlaps, and the other contribution is the existence of low-energy droplet excitations within the system. We use free boundary conditions to minimize domain-wall effects, and show that low-energy droplet excitations are the major contribution to small overlaps in numerical simulations. Free boundary conditions has stronger finite-size effects, and is likely to have the same thermodynamic limit with periodic boundary conditions.Comment: 5 pages, 4 figure

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

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.Comment: 8 pages, 5 figure

Population annealing: Theory and application in spin glasses

Population annealing is an efficient sequential Monte Carlo algorithm for simulating equilibrium states of systems with rough free energy landscapes. The theory of population annealing is presented, and systematic and statistical errors are discussed. The behavior of the algorithm is studied in the context of large-scale simulations of the three-dimensional Ising spin glass and the performance of the algorithm is compared to parallel tempering. It is found that the two algorithms are similar in efficiency though with different strengths and weaknesses.Comment: 16 pages, 10 figures, 4 table