Critical properties of the three-dimensional equivalent-neighbor model and crossover scaling in finite systems.

Abstract

Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for 12 different interaction ranges (coordination number between 18 and 250). These results allow the determination of the range dependences of the critical temperature and various critical amplitudes, which are compared to renormalization-group predictions. In addition, the analysis yields an estimate for the interaction range at which the leading corrections to scaling vanish for the spin-1 / 2 model, and confirms earlier conclusions that the leading Wegner correction must be negative for the three-dimensional (nearest-neighbor) Ising model. By complementing these results with Monte Carlo data for systems with coordination numbers as large as 52 514, the full finite-size crossover curves between classical and Ising-like behavior are obtained as a function of a generalized Ginzburg parameter. Also, the crossover function for the effective magnetic exponent is determined.