Criticality and crossover in accessible regimes

The near-critical behavior of (d=3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neig hbor interactions is studied through Monte Carlo simulations using histogra m reweighting techniques and comparisons with series expansions. By careful ly analyzing numerical data from relatively small finite systems using scal ing and extrapolation methods, it is demonstrated that one can reliably est imate critical exponents, critical temperatures, and universal amplitude ra tios, thereby distinguishing convincingly between different "nearby" univer sality classes and revealing systematic crossover effects. This study is pr eparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc.