Phase transitions in systems with non-additive long-range interactions

Abstract

We consider spin systems with long-range interactions in nonadditive regime. When the non-additive scaling limit is employed, the energy and the entropy compete and the system exhibits some phase transitions. Such systems do not satisfy the additivity, which results in some unfamiliar properties related to phase transitions. In this paper, the concept of additivity and its consequence are explained and the recent progress on statistical mechanics of long-range interacting systems are reviewed. It is shown that the parameter space is clearly decomposed into the three regions according to the stability of the uniform state predicted by the mean-field theory. Based on this parameter space decomposition, recent results on the exactness of MF theory are explained. When the interaction is non-negative (ferromagnetic), the analysis of the mean-field theory is exact and a typical spin configuration is always uniform in the canonical ensemble. However, in the restricted canonical ensemble, i.e., the canonical ensemble with a restriction of the value of the magnetization, it is shown that the mean-field theory does not necessarily give the exact description of the system and phase transitions between the mean-field uniform states (MF phase) and the inhomogeneous states (non-MF phase) occur. A new finding is that when the interaction potential changes its sign depending on the distance, the non-MF phase appears even in the canonical ensemble.

Proceedings of the STATPHYS25 conference

References in corpus (10)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Diverging equilibration times in long-range quantum spin models
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
• Negative magnetic susceptibility and nonequivalent ensembles for the mean-field ${\varphi }^4$ spin model
• Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath
• Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
• Nonadditivity in Quasiequilibrium States of Spin Systems with Lattice Distortion

Cited by in corpus (11)

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• Thermodynamics of nonadditive systems
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• Entanglement contour perspective for strong area law violation in a disordered long-range hopping model
• Long-range interacting systems in the unconstrained ensemble
• Mean-field theory is exact for the random-field model with long-range interactions
• Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
• Quantum fluctuations inhibit symmetry breaking in the HMF model
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Lattice Gas Models with Long Range Interactions
• Quasi-equilibrium nonadditivity