Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

Abstract

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality's hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected $d=3$ Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.

10 pages, 10 figures, version published in Eur. Phys. J. B

References in corpus (17)

• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Scaling Relations for Logarithmic Corrections
• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Entropic sampling via Wang-Landau random walks in dominant energy subspaces
• First-order transition features of the 3D bimodal random-field Ising model
• First order transition in a three dimensional disordered system
• Phase Diagram of the 3D Bimodal Random-Field Ising Model
• Universality in disordered systems: The case of the three-dimensional random-bond Ising model
• Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass
• Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Wang-Landau study of the 3D Ising model with bond disorder
• Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study

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• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Control of accuracy in the Wang-Landau algorithm
• Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations
• Relevance of topological disorder on the directed percolation phase transition