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 component and a conservative component, under the constraint of detailed balance, this work derives an estimation formula for the temperature-dependent magnetic induction in Ising models. Notably, the critical exponent β in the Ising model aligns well with the 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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