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We consider the Ising model on a small-world network, where the long-rangeinteraction strength $J_2$ is in general different from the local interactionstrength $J_1$, and examine its relaxation behaviors as well as phasetransitions. As $J_2/J_1$ is raised from zero, the critical temperature alsoincreases, manifesting contributions of long-range interactions to ordering.However, it becomes saturated eventually at large values of $J_2/J_1$ and thesystem is found to display very slow relaxation, revealing that orderingdynamics is inhibited rather than facilitated by strong long-rangeinteractions. To circumvent this problem, we propose a modified updatingalgorithm in Monte Carlo simulations, assisting the system to reach equilibriumquickly.Comment: 5 pages, 5 figure

Slow relaxation in the Ising model on a small-world network with strong long-range interactions