Computer simulation studies of critical phenomena

Jincheng Zhang

This paper investigates the application of computational methods to the study of critical phenomena. We explore algorithms designed to efficiently simulate systems exhibiting phase transitions, focusing on identifying and characterizing critical exponents. The core of the research centers around leveraging advancements in deep learning techniques, specifically transformer networks, diffusion models, and agent-based approaches, to accelerate the analysis of complex systems. We demonstrate how these methods can provide insights into the underlying dynamics and accurately estimate critical exponents, which are fundamental to understanding the universality of critical phenomena. The presented algorithms offer significant performance improvements over traditional methods, and the research highlights potential future directions within the field.

David Paul Landau

Jan Tobochnik

This Resource Letter provides a guide to the literature on critical point phenomena and phase transitions. Journal articles and books are cited for the following topics: continuous phase transitions, critical points, model systems with special attention to the Ising model and the Kosterlitz–Thouless transition, mean-field theory, computer simulation methods, scaling, universality, and the renormalization group.

Elmar Bittner, Wolfhard Janke E

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel-tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for two- and three-dimensional Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.

David Paul Landau