Ising-model Monte Carlo simulations: Density of states and mass gap

Abstract

We have performed Monte Carlo simulations for the three-dimensional Ising model. Using histogram techniques, we calculate the density of states on $L^3$ block lattices up to size L=14. Statistical jackknife methods are employed to perform a thorough error analysis. We obtain high-precision estimates for the leading zeros of the partition function, which, using finite-size scaling, translate into ν=0.6285±0.0019. Along a different line of approach following recent work in lattice-gauge theories, we accurately determine the mass gap m=1/ξ (ξ correlation length) for cylindrical $L^2$ $L_z$ lattices (with $L_z$=256 and L up to 12). The finite-size-scaling analysis of the mass-gap data leads to ν=0.6321±0.0019.