Series and Monte Carlo study of high-dimensional Ising models

Ising models in high dimensions are used to compare high-temperature series expansions with Monte Carlo simulations. Simulations of the magnetization on four-, six-, and seven-dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data for d=6 and 7. We tabulate 15 terms of series expansions for the susceptibility for general d and give J/k_BT_c=0.092295 (3) and 0.077706 (2) for d=6 and 7. In contrast to five dimensions, where earlier series found nonanalytic scaling corrections, for d=6 and 7 the leading scaling correction may be analytic in T-T_c. In most cases these expansions gave more accurate results than these simulations.