Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness

Abstract

We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with ν=1.30(6) and β/ν=0.128(5). This amounts to a strong violation of the universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two transitions supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.

Added discussion and references. 10 pages, 6 figures. Published version

References in corpus (9)

• Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models
• Entropic sampling via Wang-Landau random walks in dominant energy subspaces
• First-order transition features of the 3D bimodal random-field Ising model
• The Blume-Emery-Griffiths Spin Glass and Inverted Tricritical Points
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions
• Monte-Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang-Landau algorithm
• Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems
• Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions

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