Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

Abstract

It was recently shown [Phys. Rev. Lett. {\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent $\alpha$ of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

16 pages, 9 figures, 2 tables, final version to be published in Phys. Rev. E

References in corpus (18)

• Critical parameters of the three-dimensional Ising spin glass
• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Critical behavior of colloid-polymer mixtures in random porous media
• First-order transition features of the 3D bimodal random-field Ising model
• Finite size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
• First order transition in a three dimensional disordered system
• Destruction of first-order phase transition in a random-field Ising model
• Phase Diagram of the 3D Bimodal Random-Field Ising Model
• Wang-Landau study of the critical behaviour of the bimodal 3D-Random Field Ising Model
• The random field Ising model with an asymmetric trimodal probability distribution
• Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point
• First excitations in two- and three-dimensional random-field Ising systems
• Scale Invariance and Self-averaging in disordered systems
• Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions
• Diluted Antiferromagnetic 3D Ising model in a field
• On the phase transition of the 3D random field Ising model
• Scaling, domains, and states in the four-dimensional random field Ising magnet

Cited by in corpus (24)

• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Review of recent developments in the random-field Ising model
• Universality from disorder in the random-bond Blume-Capel model
• Statistical mechanics of coupled supercooled liquids in finite dimensions
• Random-field Ising model criticality in a glass-forming liquid
• Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field
• The Effect of Confinement on Capillary Phase Transition In Granular Aggregates
• Finite-size scaling of the random-field Ising model above the upper critical dimension
• Critical behavior of the spin-3/2 Blume Capel quantum model with two random transverse single-ion anisotropies
• Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model
• Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model
• Suppression of spinodal instability by disorder in an athermal system
• Critical exponent $\nu$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
• Dimensional reduction and its breakdown in the driven random field O(N) model
• Finite-dimensional signature of spinodal instability in an athermal hysteretic transition
• On the critical exponent $\alpha$ of the 5D random-field Ising model
• Rejection-free Glauber Monte Carlo for the 2D Random Field Ising Model via Hierarchical Probabilistic Counters
• Efficient algorithms for computing ground states of the 2D random-field Ising model
• The Schwartz-Soffer and more inequalities for random fields
• Understanding jump discontinuity in disordered system
• Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields
• Universality in the two-dimensional dilute Baxter-Wu model