Effect of long-range interactions on the critical behavior of the continuous Ising model

Critical behavior of the one- and two-dimensional general continuous Ising models with long-range ferromagnetic interactions decaying as 1/r(d+sigma) is studied using a histogram Monte Carlo technique. A continuous Ising model means that a spin can take any value between -1 and 1. It is found that the system;exhibits a second-order phase transition with nonstandard critical exponents which depend on sigma. Results for Various values of sigma Will be shown and compared to predictions from renormalization-group theory. Though there is an agreement with the overall tendency predicted, there are several fundamental differences. Discussion is given. [S0163-1829(99)02718-6].