Critical parameters of the three-dimensional Ising spin glass

Abstract

We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L = 40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain T c = 1.1019(29) for the critical temperature, ν = 2.562(42) for the thermal exponent, η = −0.3900(36) for the anomalous dimension, and ω = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α = −5.69(13), β = 0.782(10), and γ = 6.13(11). We also compute several universal quantities at T c .

Gardner transition in finite dimensions

“…Thus, reasoning only in terms of phases and type of symmetry breaking one would conclude that spin-glasses in a field and low temperature/high pressure glasses are in the same universality class both for the transition, Gardner versus spin-glass, and the properties of the FRSB phase. This would be also what one would conclude from the works by Moore and collaborators [33][34][35], in which the glass transition was argued to be related to the spin-glass transition in a field (see also [36]). As we shall show, however, the situation is more intricate and need further analysis.…”

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

“…We should note that previous applications of the method include diluted antiferromagnets [48] and the spin-glass problem; see Ref. [108] and references therein.…”

Out-of-equilibrium finite-size method for critical behavior analyses

“…Essentially all runs end when the system is still out of equilibrium. In most of the cases, data extend only up R ξ ≈ 0.5, in some cases even less (at equilibrium [3] R ξ = 0.652(3) at the critical point). Simulations were performed on a small graphics processing unit (GPU) cluster using a very efficient asynchronous multispin coding technique [20].…”

“…Four cumulants defined here are directly related to those used in Ref. [3]. If U 4,J , U 22,J , U 111,J , and U 1111,J are the quantities defined in Ref.…”

“…Moreover, equilibration times depend strongly on the disorder realization, so that a sample-by-sample analysis is needed to guarantee that all measurements are obtained from well-equilibrated samples [2]. At present, even by using dedicated machines [3], it seems impossible to go much beyond sizes L = 30 − 40.…”