Mutual information in classical spin models

Abstract

The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high temperature paramagnetic phase. The Shannon and Renyi mutual information in both Ising and Potts models in 2 dimensions are calculated numerically by combining matrix product states algorithms and Monte Carlo sampling techniques.

References in corpus (8)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix product states represent ground states faithfully
• The ALPS project release 1.3: open source software for strongly correlated systems
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• Criticality, the area law, and the computational power of PEPS
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions

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• Area law violation for the mutual information in a nonequilibrium steady state
• Detecting Classical Phase Transitions with Renyi Mutual Information
• Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model
• Information theoretic aspects of the two-dimensional Ising model
• Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model
• Machine-learning Iterative Calculation of Entropy for Physical Systems
• Generalized mutual informations of quantum critical chains
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• Statistical physics through the lens of real-space mutual information
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• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• Information theoretic approach to ground-state phase transitions for two and three-dimensional frustrated spin systems
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• Entanglement measures and the quantum to classical mapping
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• Landauer current and mutual information in a bosonic quantum dot
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• Mutual information in interacting spin systems
• A computational mechanics approach to estimate entropy and (approximate) complexity for the dynamics of the 2D Ising Ferromagnet
• Multiscale complexity of two-dimensional Ising systems with short-range, ferromagnetic interactions