Phase transition of a one-dimensional Ising model with distance-dependent connections

The critical behavior of the Ising model on a one-dimensional network, which has long-range connections at distances l>1 with the probability Theta(l)similar to l(-m), is studied by using Monte Carlo simulations. Through analyzing the Ising model on networks with different m values, this paper discusses the impact of the global correlation, which decays with the increase of m, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter [< M >], it is observed that in the whole range of 0 < m < 2, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.