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+σ, in dimension d0ex0ex=0ex0ex1, 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 σ, from qc0ex0ex=0ex0ex8 for σ0ex0ex=0ex0ex1 to qc0ex0ex=0ex0ex2 for σ0ex0ex=0ex0ex0.3. Detailed results for various σ will be shown and discussed. Mean-field calculation confirms the tendency of our MC results.