Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study

Abstract

Using recently developed histogram techniques and an ultrafast multispin coding simulation algorithm, we have investigated the critical behavior of the d=3 simple-cubic Ising model. We have studied lattice sizes ranging from L=8 to 96 using between 3×${10}^6$ and 12×${10}^6$ Monte Carlo steps (complete lattice updates). By accurately measuring the finite-size behavior of several different thermodynamic quantities, we are able to determine the critical properties with a precision comparable to that obtained with Monte Carlo renormalization-group and sophisticated series-expansion techniques. The best estimate of the inverse critical temperature from our analysis is ${\mathit{K}}_{\mathit{c}}$=0.221 659 5±0.000 002 6. The advantages of the histogram technique are discussed, as are the potential problems that can arise at this level of resolution.