Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model

While no analytic solution for the 3d Ising model exists, various numerical methods such as series expansion, Monte Carlo and MCRG have provided precise information about the phase transition. [1] Applying Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators, and analyzing data with histogram reweighting techniques and quadruple precision arithmetic, we have investigated the critical behavior of the 3d Ising Model, with lattice sizes ranging from 16³ to 1024³. By analyzing data with cross-correlations [2] between various thermodynamic quantities obtained from the same data pool, e.g. logarithmic derivatives of magnetization and energy cumulant, [3] we have obtained the critical inverse temperature K_c = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86), and we will compare our results with the latest theoretical predictions.


[1] For an overview of earlier work, see A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002)
[2] M. Weigel and W. Janke, Phys. Rev. E 81, 06672 (2010)
[3] A. M. Ferrenberg and D. P. Landau, Phys. Rev. B 44, 5081 (1991)