Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems

Abstract

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called "exactness of the mean-field theory". It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the α-Potts model with annealed vacancies and the α-Potts model with invisible states.

23 pages, to appear in J. Stat. Phys

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Phase Transition in Potts Model with Invisible States
• Ensemble Inequivalence and the Spin-Glass Transition

Cited by in corpus (11)

• Phase transitions in systems with non-additive long-range interactions
• Potts Model with Invisible States: A Review
• Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
• Marginal dimensions of the Potts model with invisible states
• Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
• Transformer Wave Function for Quantum Long-Range models
• Ising model with invisible states on scale-free networks
• Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
• Lattice Gas Models with Long Range Interactions
• Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics
• Quasi-equilibrium nonadditivity