Monte Carlo tests of theoretical predictions for critical phenomena: stilla problem?

Two Monte Carlo studies of critical behavior in ferromagnetic Ising models are described: the first one deals with the crossover from the Ising class to the mean field class, when the interaction range increases. The second s tudy deals with the finite size behavior at dimensionalities above the marg inal dimension where Landau theory applies. The numerical results are compa red to pertinent theoretical predictions, and unsolved problems are briefly described. (C) 2000 Elsevier Science B.V. All rights reserved.