Phase transition in a general continuous Ising model with long-range interactions

Critical exponents for a one-dimensional general continuous Ising model with long-range ferromagnetic interactions decaying as 1/r(1+sigma) are calculated using a histogram Monte Carlo technique. A continuous Ising model means that a spin can take any value between -1 and 1. The critical point behavior is investigated. It is found that the system exhibits a second-order phase transition with nonstandard critical exponents; the singularities in the specific heat and susceptibility depend on sigma. For sigma=1, there are extremely weak finite size effects: the first-order and the second-order cumulants of the order parameter yield nu=2.42(1). The susceptibility exponent gamma=2.259(9). Results for sigma=0.7 will be shown and discussed. (C) 1999 American Institute of Physics. [S0021-8979(99)28608-2].