In-Depth Investigation of Phase Transition Phenomena in Network Models Derived from Lattice Models

TL;DR

This paper introduces a Monte Carlo-based network modeling approach to analyze phase transitions in lattice models, successfully estimating critical points and exponents with high accuracy.

Contribution

It presents a novel network transformation framework for lattice models, enabling detailed phase transition analysis and precise estimation of critical parameters.

Findings

Accurately estimates the critical temperature with only 0.7% deviation.

Aligns the critical exponent β with established theoretical values.

Provides a new analytical approach for complex lattice models.

Abstract

Lattice models exhibit significant potential in investigating phase transitions, yet they encounter numerous computational challenges. To address these issues, this study introduces a Monte Carlo-based approach that transforms lattice models into a network model with intricate inter-node correlations. This framework enables a profound analysis of Ising, JQ, and XY models. By decomposing the network into a maximum entropy and a conservative component, under the constraint of detailed balance, this work derive an estimation formula for the temperature-dependent magnetic induction in Ising models. Notably, the critical exponent $\beta$ in the Ising model aligns well with established results, and the predicted phase transition point in the three-dimensional Ising model exhibits a mere $0.7 \%$ deviation from numerical simulations.