Potts model with long-range interactions in one dimension

We study the nature of the phase transition of the q-state Potts model with long-range ferromagnetic interactions decaying as 1/r(d+sigma), in dimension d = 1, using a histogram Monte Carlo (MC) technique. The model can exhibit a first-order transition or a second-order phase transition with nonstandard critical exponents. The critical value of q above which a first-order transition occurs decreases with decreasing sigma, from q(c) = 8 for sigma = 1 to q(c) = 2 for sigma = 0.3. Detailed results for various sigma will be shown and discussed. Mean-field calculation confirms the tendency of our MC results.