Shared information in classical mean-field models
arXiv:1409.5520 · doi:10.1088/1751-8113/48/5/055002
Abstract
Universal scaling of entanglement estimators of critical quantum systems has drawn a lot of attention in the past. Recent studies indicate that similar universal properties can be found for bipartite information estimators of classical systems near phase transitions, opening a new direction in the study of critical phenomena. We explore this subject by studying the information estimators of classical spin chains with general mean-field interactions. In our explicit analysis of two different bipartite information estimators in the canonical ensemble we find that, away from criticality both the estimators remain finite in the thermodynamic limit. On the other hand, along the critical line there is a logarithmic divergence with increasing system-size. The coefficient of the logarithm is fully determined by the mean-field interaction and it is the same for the class of models we consider. The scaling function, however, depends on the details of each model. In addition, we study the information estimators in the micro-canonical ensemble, where they are shown to exhibit a different universal behavior. We verify our results using numerical calculations of two specific cases of the general Hamiltonian.
7 figures, 37 pages, submitted to J. Phys. A
References in corpus (11)
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Area laws in quantum systems: mutual information and correlations
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Entanglement spectrum in one-dimensional systems
- Kitaev chains with long-range pairing
- Entanglement scaling in critical two-dimensional fermionic and bosonic systems
- Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
- Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
- Information theoretic aspects of the two-dimensional Ising model
- Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
- Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point