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arXiv · 2405.15233

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

Yonglong Ding
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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.

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BibTeXRIS

Yonglong Ding. 2024-05-24. In-Depth Investigation of Phase Transition Phenomena in Network Models Derived from Lattice Models. https://doi.org/10.1063/5.0219207

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