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The critical scaling behavior of Ising models with long range interactions is studied. These long-range interactions, when imposed in addition to interactions on a regular lattice, lead to small world graphs. Large-scale Monte Carlo simulations, together with finite-size scaling, is used to obtain the critical behavior of a number of different models. These include the z-model introduced by Scalettar, standard small-world bonds superimposed on a square lattice, and physical small-world bondsdoi:10.1590/s0103-97332006000500016 fatcat:vxdrspek6nfr3k5uqxm2qv5weq