The critical behavior of Ising model on a one-dimensional network, which has
long-range connections at distances l>1 with the probability Θ(l)∼l−m, is studied by using Monte Carlo simulations. Through studying 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 [], 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.Comment: 5 pages,8 figure