Critical behavior of the Ising and Blume-Capel models on directed two-dimensional small-world networks
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The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p c , and a first-order phase transition for p > p c , where p c ≈ 0.25. The critical exponents for p < p c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.
KeywordsStatistical and Nonlinear Physics
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