The authors use Monte Carlo simulations to estimate for the first time the corner critical exponents for the three-dimensional Ising model with a free boundary condition at bulk criticality. Finite-size dependences of the spin-spin correlation functions are used to obtain η bulk-corner = 1.75 ± 0.2.
We present the first Monte Carlo estimate of the edge critical exponent ${\ensuremath{\Delta}}_{2}$ for the three-dimensional nearest-neighbor ferromagnetic Ising model at the ordinary edge transition. The finite-size dependence of the spin-spin correlation function is used to obtain the edge-bulk exponent ${\ensuremath{\eta}}_{0}$,2=1.704\ifmmode\pm\else\textpm\fi{}0.1, and this gives ${\ensuremath{\Delta}}_{2}$/${\ensuremath{\nu}}_{b}$=-1.185\ifmmode\pm\else\textpm\fi{}0.1. This last value is in agreement with the \ensuremath{\epsilon}-expansion estimate of -29/24=-1.208. . . .
We present an extensive Monte Carlo study of the three-dimensional Ising model with free surfaces, edges, and corners at bulk criticality. Finite-size scaling properties of the excess free energies of free surfaces, edges, and corners are estimated by use of the recently proposed applications of the parametric integration method. The corner excess free energies are obtained for the first time and are consistent with the logarithmic finite-size scaling predictions. Results of the simplecubic and body-centered-cubic lattices provide support for the proposed universality of the finite-size scaling amplitudes for the excess free energies of free surfaces, edges, and corners.
We report the results of a Monte Carlo investigation of the (equilibrium) time-displaced correlation functions for the magnetization and energy of a simple cubic Ising model as a function of time, temperature, and lattice size. The simulations were carried out on a CDC CYBER 205 supercomputer employing a high-speed, vectorized multispin coding program and using a total of 5\ifmmode\times\else\texttimes\fi{}1012 Monte Carlo spin-flip trials. We used L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L lattices with periodic boundary conditions and L as large as 96. The short-time and long-time behaviors of the correlation functions are analyzed by fits to a sum of exponential decays, and the critical exponent z for the largest relaxation time is extracted using a finite-size-scaling analysis. Our estimate z=2.04\ifmmode\pm\else\textpm\fi{}0.03 resolves an intriguing contradiction in the literature; it satisfies the theoretical lower bound and is in agreement with the prediction obtained by \ensuremath{\epsilon} expansion. We also consider various small systematic errors that typically occur in the analysis of relaxation functions and show how they can lead to spurious results if sufficient care is not exercised.
We used a Monte Carlo simulation of the structurally disordered three dimensional Ising model. For the systems with spin concentrations p = 0.95 ,0.8, 0.6 and 0.5 we calculated the correlation-length critical exponent ν by finite-size scaling. Extrapolations to the thermodynamic limit yield ν(0.95) = 0.705(5) ,ν(0.8) = 0.711(6),ν(0.6) = 0.736(6) and ν(0.5) = 0.744(6). These results are compatible with some previous estimates from a variety of sources. The analysis of the results demonstrates the nonuniversality of the critical behavior in the disordered Ising model.
We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin glass models: the ± J Ising model for two values of the disorder parameter p , p = 1/2 and 0.7, and the bond-diluted ± J model for bond-occupation probability p b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent ω related to the leading irrelevant operator, ω = 1.0(1). We also determine the critical exponents ν and η. Taking into account the scaling corrections, we obtain ν = 2.53(8) and η = −0.384(9).