The CrMES scheme as an alternative to Importance Sampling: The tail regime of the order-parameter distribution

TL;DR

This paper introduces the CrMES scheme as an efficient alternative to importance sampling for estimating critical behavior and tail distributions in statistical models, demonstrated on the 2D Ising model.

Contribution

The paper develops and applies the CrMES entropic sampling scheme combined with Wang-Landau sampling to improve critical exponent estimation and analyze the tail regime of the order-parameter distribution.

Findings

CrMES-WL sampling accurately estimates critical properties.

The method effectively explores the tail regime of the order-parameter distribution.

Provides a comprehensive alternative to traditional importance sampling and Metropolis algorithms.

Abstract

We review the recently developed critical minimum energy-subspace (CrMES) technique. This scheme produces an immense optimization of popular algorithms, such as the Wang-Landau (WL) and broad histogram methods, by predicting the essential part of the energy space necessary for the estimation of the critical behavior and provides a new route of critical exponent estimation. A powerful and efficient CrMES entropic sampling scheme is proposed as an alternative to the traditional importance sampling methods. Utilizing the WL random walk process in the dominant energy subspace (CrMES-WL sampling) and using the WL approximation of the density of states and appropriate microcanonical estimators we determine the magnetic properties of the 2D Ising model. Updating $(E,M)$ histograms during the high level WL-iterations, we provide a comprehensive alternative scheme to the Metropolis algorithm and by applying this procedure we present a convincing analysis for the far tail regime of the order-parameter probability distribution.