Critical exponents for a one-dimensional general continuous Ising model wit
h long-range ferromagnetic interactions decaying as 1/r(1+sigma) are calcul
ated using a histogram Monte Carlo technique. A continuous Ising model mean
s that a spin can take any value between -1 and 1. The critical point behav
ior is investigated. It is found that the system exhibits a second-order ph
ase transition with nonstandard critical exponents; the singularities in th
e specific heat and susceptibility depend on sigma. For sigma=1, there are
extremely weak finite size effects: the first-order and the second-order cu
mulants of the order parameter yield nu=2.42(1). The susceptibility exponen
t gamma=2.259(9). Results for sigma=0.7 will be shown and discussed. (C) 19
99 American Institute of Physics. [S0021-8979(99)28608-2].