Eur. Phys. J. B (2013) 86: 300
https://doi.org/10.1140/epjb/e2013-40165-5

Regular Article

Critical behavior of the Ising and Blume-Capel models on directed two-dimensional small-world networks

¹ Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550 Teresina, PI, Brazil
² Departamento de Física, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte, MG, Brazil
³ Center for Simulational Physics, University of Georgia, 30602 Athens-GA, USA
⁴ Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP Oxford, England

^a e-mail: pla@hal.physast.uga.edu

Received: 26 February 2013
Received in final form: 25 April 2013
Published online: 1 July 2013

Abstract

The critical properties of the two-dimensional Ising and Blume-Capel model on directed small-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 directed small-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 directed small-world lattice.