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

TL;DR

This paper investigates the critical properties and crossover behavior of the three-dimensional equivalent-neighbor model across various interaction ranges, providing numerical data that align with renormalization-group predictions and elucidate finite-size effects.

Contribution

It offers detailed numerical analysis of the 3D equivalent-neighbor model for multiple interaction ranges, including finite-size crossover curves and critical amplitude dependencies.

Findings

Critical temperature and amplitudes depend on interaction range.

Identification of the interaction range where leading corrections vanish.

Full crossover curves between classical and Ising-like behavior obtained.

Abstract

Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve 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 52514, 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.