Critical behavior of the spin-1 Blume-Capel model on two-dimensional Voronoi-Delaunay random lattices

F. P. Fernandes, Douglas F. de Albuquerque, F. W. S. Lima, and J. A. Plascak
Phys. Rev. E 92, 022144 – Published 26 August 2015

Abstract

The critical properties of the spin-1 Blume-Capel model in two dimensions is studied on Voronoi-Delaunay random lattices with quenched connectivity disorder. The system is treated by applying Monte Carlo simulations using the heat-bath update algorithm together with single histograms re-weighting techniques. We calculate the critical temperature as well as the critical exponents as a function of the crystal field Δ. It is found that this disordered system exhibits phase transitions of first- and second-order types that depend on the value of the crystal field. For values of Δ3, where the nearest-neighbor exchange interaction J has been set to unity, the disordered system presents a second-order phase transition. The results suggest that the corresponding exponent ratio belongs to the same universality class as the regular two-dimensional ferromagnetic model. There exists a tricritical point close to Δt=3.05(4) with different critical exponents. For ΔtΔ<3.4 this model undergoes a first-order phase transition. Finally, for Δ3.4 the system is always in the paramagnetic phase.

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  • Received 3 December 2014
  • Revised 26 June 2015

DOI:https://doi.org/10.1103/PhysRevE.92.022144

©2015 American Physical Society

Authors & Affiliations

F. P. Fernandes1, Douglas F. de Albuquerque1,2, F. W. S. Lima3, and J. A. Plascak3,4,5,6

  • 1Departamento de Física, Universidade Federal de Sergipe, 49100-000, São Cristovão, SE, Brazil
  • 2Departamento de Matemática, Universidade Federal de Sergipe, 49100-000 São Cristovão, SE, Brazil
  • 3Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina, PI, Brazil
  • 4Universidade Federal da Paraíba, Centro de Ciências Exatas e da Natureza - Campus I, Departamento de Física - CCEN Cidade Universitária 58051-970 - João Pessoa, PB - Brazil
  • 5Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA
  • 6Departamento de Física, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, MG, Brazil

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Vol. 92, Iss. 2 — August 2015

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