Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
arXiv:1410.1279 · doi:10.1088/1751-8113/48/14/145001
Abstract
The existence of the thermodynamic limit in spin systems with short- and long-range interactions is established. We consider the infinite-volume limit with a fixed shape of the system. The variational expressions of the entropy density and the free energy density are obtained, which explicitly depend on the shape of the system. This shape dependence of thermodynamic functions implies the nonadditivity, which is one of the most important characteristics of long-range interacting systems.
arXiv comment24 pages, 2 figures
References in corpus (20)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
- Breaking of ergodicity and long relaxation times in systems with long-range interactions
- An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
- Large deviation techniques applied to systems with long-range interactions
- Long-range interactions and non-extensivity in ferromagnetic spin models
- Canonical solution of a system of long-range interacting rotators on a lattice
- Canonical Solution of Classical Magnetic Models with Long-Range Couplings
- Quasi-stationary states and the range of pair interactions
- Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
- Analysis of the exactness of mean-field theory in long-range interacting systems
- Asymptotic forms and scaling properties of the relaxation time near threshold points in spinodal-type dynamical phase transitions
- Scaling properties of the relaxation time near the mean-field spinodal
- Instability of the mean-field states and generalization of phase separation in long-range interacting systems
- Crossover between a Short-range and a Long-range Ising model
- A dynamical classification of the range of pair interactions
- Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
- Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
- Nonadditivity in Quasiequilibrium States of Spin Systems with Lattice Distortion
- Microcanonical analysis of the Curie-Weiss anisotropic quantum Heisenberg model in a magnetic field