We consider the Ising model on a small-world network, where the long-range
interaction strength J2 is in general different from the local interaction
strength J1, and examine its relaxation behaviors as well as phase
transitions. As J2/J1 is raised from zero, the critical temperature also
increases, manifesting contributions of long-range interactions to ordering.
However, it becomes saturated eventually at large values of J2/J1 and the
system is found to display very slow relaxation, revealing that ordering
dynamics is inhibited rather than facilitated by strong long-range
interactions. To circumvent this problem, we propose a modified updating
algorithm in Monte Carlo simulations, assisting the system to reach equilibrium
quickly.Comment: 5 pages, 5 figure