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

We have performed Monte Carlo simulations for the three-dimensional Ising model. Using histogram techniques, we calculate the density of states on L³ 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 L²{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.