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

9 pages, 4 figures

References in corpus (24)

• Quantum Monte Carlo methods for nuclear physics
• Continuous Time Quantum Monte Carlo method for fermions
• The nonperturbative functional renormalization group and its applications
• Learning to Simulate Complex Physics with Graph Networks
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• A Practical Guide to Surface Kinetic Monte Carlo Simulations
• Combinatorial Optimization with Physics-Inspired Graph Neural Networks
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Antiferromagnetically ordered Mott insulator and $d+id$ superconductivity in twisted bilayer graphene: A quantum Monte carlo study
• Efficient simulation of moire materials using the density matrix renormalization group
• The role of electron-electron interactions in two-dimensional Dirac fermions
• Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances
• Low communication high performance ab initio density matrix renormalization group algorithms
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Extension to order ${\beta }^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
• A Projector Quantum Monte Carlo Method for non-linear wavefunctions
• Density Matrix Renormalization Group with Tensor Processing Units
• FPGA Hardware Acceleration of Monte Carlo Simulations for the Ising Model
• Quantum Monte Carlo study of superconductivity in rhombohedral trilayer graphene under an electric field
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Many-variable variational Monte-Carlo study of superconductivity in two-band Hubbard models with an incipient band
• First order phase transitions in the square lattice "easy-plane" J-Q model
• High Performance Monte Carlo Simulation of Ising Model on TPU Clusters