The authors study the Ising spin glass with a +or-J distribution in six dimensions by Monte Carlo simulations. Their results for the transition temperature agree very well with the value from series expansions. The exponents are consistent with mean-field values modified by logarithmic corrections as expected.
The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having \ifmmode\pm\else\textpm\fi{}J distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3\ensuremath{\le}L\ensuremath{\le}20. Results for the probability distribution, PL(q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at Tc${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.
We investigate the order-parameter distribution P(q) of the Ising spin glass with nearest-neighbor interactions in four dimensions using Monte Carlo simulations on lattices of linear dimension up to L=6. We find that, below the transition temperature Tc, the weight at small q seems to saturate to a nonzero value as the size increases, similar to the infinite-range Sherrington-Kirkpatrick model. We discuss our results in the light of recent theoretical predictions for the nature of the spin-glass phase.
We have studied the three-dimensional Ising spin glass with a $\ifmmode\pm\else\textpm\fi{}J$ distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite-size scaling analysis shows quite strong evidence for a finite transition temperature Tc with ordering below Tc. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent $\ensuremath{\nu}$ is somewhat higher. Because there may be (unknown) corrections to finite-size scaling, we do not completely rule out the possibility that Tc=0 or that Tc is finite but with no order below Tc. However, from our data, these possibilities seem less likely.
We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.
We present the results of numerical simulations on Ising spin glasses in zero magnetic field with nearest-neighbor interactions on hyper-cubic lattices in two, three, and four dimensions with both Gaussian and \ifmmode\pm\else\textpm\fi{}J bond distributions. Finite-size scaling is used to analyze the results. In two dimensions (d=2) we agree with earlier work that the transition temperature is at Tc=0, and obtain the correlation-length exponent \ensuremath{\nu}, and the exponent \ensuremath{\eta}, at the zero-temperature transition for the \ifmmode\pm\else\textpm\fi{}J model. In d=3 dimensions we concentrate on results for the Gaussian distribution, since our results for the \ifmmode\pm\else\textpm\fi{}J distribution have been presented earlier. As expected, we find similar results for the two distributions, namely a nonzero Tc but evidence that d=3 is close to the lower critical dimension. In a four-dimensional spin glass with Gaussian bonds we find that only a modest amount of computer time is required to show that Tc is nonzero with a long-range-ordered phase below Tc. Our estimates for critical exponents in d=4 dimensions agree well with results from recent high-temperature-series expansions.