Search for a transition in the three-dimensional J Ising spin-glass

Abstract

The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having a ± / distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3 ^L ^20. Results for the probability distribution, PL(Q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T ^ 1.2 are consistent with a conventional phase transition at 7^ = 1.210.2. with exponents v = 1.3 ±0.3 and r)= -0.3 ±0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.

Critical behavior of three-dimensional Ising spin glass models

“…28 They are all in substantial agreement with our result, which is however significantly more precise. We also mention the estimate β = 0.52 (9), obtained in Ref. 26 by an out-of-equilibrium simulation.…”

“…To fix β max we used the results of Ref. 30, which provided the best estimates of R * ξ at the time we started our simulations: (6) 1.48193 (6) 1.50300 (9) 1.49618 (9) 1.50788 (9) 1.5033(2) 7 1.49753 (6) 1.48642 (6) 1.50544(9) 8 1.49987 (6) 1.48984 (6) 1.50714 (9) 1.50082 (9) 1.51320 (13) 1.5063(5) 9 1.50136 (6) 1.49260 (6) 1.50815(9) 10 1.50273 (6) 1.49478 (6) 1.50889 (9) 1.50382 (11) 1.5146(2) 11 1.50383 (6) 1.49665 (6) 1.50946(9) 12 1.50469 (6) 1.49781 (7) 1.50984 (13) (3) 1.5048(5) 24 1.5089(4) 28 1.5108 (13) 0.627(4) and 0.635 (9) for an Ising model with bimodal and Gaussian distributed bonds, respectively. Thus, in most of the runs β max was chosen so that R ξ (β max , L) ≈ 0.63.…”

“…to belong to a universality class which is independent of the details of the model and, in particular, of the disorder distribution. Several numerical works 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33 have addressed these issues, considering various Ising spin-glass models, characterized by different disorder distributions, with or without dilution. Over the years many estimates of the critical exponents have been obtained.…”

Fluctuation-dissipation ratio in three-dimensional spin glasses

“…In this model a phase transition has been observed at T c ≈ 1.2 [14] (see however [15] for a different point of view). We use single-spin-flip heat-bath dynamics with parallel sublattice update and calculate the spin-autocorrelation function C(τ, t w ) (in zero field) and the thermoremanent magnetization M(τ + t w , t w ) as defined in (4).…”

Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions

“…Here we consider the correlation length of the SG component of the spin, i.e., S i (≡ S i − m) with m as the ferromagnetic component of m = i x i S i /(xN ). We perform a cooling simulation of a two-replica system with {S i } and {T i } [27]. The SG order parameter, generalized to wave vector k, q µν (k), is defined as…”