  The critical behavior of Ising model on a one-dimensional network, which has
long-range connections at distances $l>1$ with the probability $\Theta(l)\sim
l^{-m}$, 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 $[< M>]$, 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.
