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

TLDR

The study employed Monte Carlo simulations on simple‑cubic lattices of size L = 8–96, performing 3–12 million full‑lattice updates per run. Using high‑resolution histogram Monte Carlo simulations, the authors accurately determined the 3D Ising critical temperature Kc = 0.2216595(26) and other critical properties with precision rivaling renormalization‑group and series‑expansion methods, while also highlighting the strengths and limitations of the histogram approach.

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\ifmmode\times\else\texttimes\fi{}${10}^{6}$ and 12\ifmmode\times\else\texttimes\fi{}${10}^{6}$ 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\ifmmode\pm\else\textpm\fi{}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.