Theory of Order-Disorder Phase Transitions Induced by Fluctuations Based on Network Models

TL;DR

This paper presents a network-based theoretical framework explaining how fluctuations induce order-disorder phase transitions, deriving critical points and exponents, and validating with classical models like Ising and Edwards-Anderson.

Contribution

It introduces a novel network model approach to analyze phase transitions driven by fluctuations, providing explicit formulas and validation for classical models.

Findings

Derived high-order detailed balance relationships for correlated systems.

Obtained phase transition points and critical exponents.

Validated theory with Ising and Edwards-Anderson models.

Abstract

Both quantum phase transitions and thermodynamic phase transitions are probably induced by fluctuations, yet the specific mechanism through which fluctuations cause phase transitions remains unclear in existing theories. This paper summarizes different phases into combinations of three types of network structures based on lattice models transformed into network models. These three network structures correspond to ordered, boundary, and disordered conditions, respectively. By utilizing the transformation relationships satisfied by these three network structures and classical probability, this work derive the high-order detailed balance relationships satisfied by strongly correlated systems. Using the high-order detailed balance formula, this work obtain the weights of the maximum entropy network structures in general cases. Consequently, I clearly describe the process of ordered-disordered phase transitions based on fluctuations and provide critical exponents and phase transition points. Finally, I verify this theory using the Ising model in different dimensions, the frustration scenario of the triangular lattice antiferromagnetic Ising model, and the expectation of ground-state energy in the two-dimensional Edwards-Anderson model.