Ising model on a small world network

A one-dimensional Ising model is studied, via Monte Carlo simulations, on a small world network, where each site has, apart from couplings to its two nearest neighbors, a certain probability to be linked to one of its farther neighbors. It is demonstrated that even a small fraction of such links enables the system to order at finite temperatures. The critical exponent $\beta$ is smaller than the two-dimensional value, and seems to be independent of the concentration of the extra links. The dependence of the magnetization and the critical temperature on the concentration of the small world links is also presented.