Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study

Abstract

We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80-140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high-levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.

24 pages, 5 figures

References in corpus (15)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Understanding and Improving the Wang-Landau Algorithm
• Transition Matrix Monte Carlo Method
• Avoiding Boundary Effects in Wang-Landau Sampling
• Transition Matrix Monte Carlo Reweighting and Dynamics
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study
• Minimum Decision Cost for Quantum Ensembles
• Flat Histogram Method of Wang-Landau and N-fold Way
• Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?
• Universal features of the order-parameter fluctuations : reversible and irreversible aggregation
• Estimation of critical behavior from the density of states in Classical Statistical Models
• Entropic sampling via Wang-Landau random walks in dominant energy subspaces

Cited by in corpus (5)

• Phase Diagram of the 3D Bimodal Random-Field Ising Model
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
• Universal and non-universal signatures in the scaling functions of critical variables