Scaling relationship between effective critical exponents throughout the crossover region in thin Ising films

The Monte Carlo (MC) approach is used to check the validity of the scaling relationship gamma = beta(delta - 1) for the effective critical exponents i n thin Ising films. We investigate this relationship not just in the critic al region but throughout the crossover to the expected two-dimensional beha vior. Our results indicate that this scaling relationship is very well-fulf illed throughout the entire crossover temperature region, as predicted by a previous renormalization group analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for L x L x D plates with increasing L, up to L = 100. The evolution of the maximu m value of the effective critical exponents with film thickness is discusse d.