Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

2010/01/08 by A. Malakis, A. Nihat Berker, I. A. Hadjiagapiou +5 · 73 citations
Materials Science · Mathematics · Physics and Astronomy · #Computer science #Condensed matter physics #Critical exponent #Crossover #Ferromagnetism #Ising model #Magnetic properties of thin films #Material Dynamics and Properties #Mathematics #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Randomness #Renormalization group #Square lattice #Statistical physics #Statistics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.81.041113

published in Physical Review E 81(4), 041113 (American Physical Society) · 12 pages, 11 figures, submitted for publication

arxiv created 2010/01/08 · openalex publication_date 2010/04/15 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase-transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double-logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.

Citations

• Multicriticality in the Blume–Capel model under a continuous-field probability distribution
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach
• Finite-size scaling study of the two-dimensional Blume-Capel model
• Effect of random defects on the critical behaviour of Ising models
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• The quenched-disordered Ising model in two and four dimensions

Cited by

• Nonconvergence of the Wang-Landau algorithms with multiple random walkers
• Correlations equalities and some upper bounds for the critical temperature for spin one systems
• A comparative review of recent results on supercritical anomalies in two-dimensional kinetic Ising and Blume-Capel ferromagnets

Related

• Universality aspects of the d=3 random-bond Blume-Capel model
• Mean-field solution of the Blume-Capel model under a random crystal field
• Wang–Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions
• Multicriticality in the Blume–Capel model under a continuous-field probability distribution
• Pseudo Transitions in the Finite-Size Blume-Capel Model