Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions

Abstract

We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the paramagnetic and spin glass or ferromagnetic phases for $p\ge 5$. In the parameter region around the first-order transitions, the solutions give different results depending on the ensemble used for the analysis. In particular, we observe that the microcanonical specific heat can be negative and the phase may not be uniquely determined by the temperature.

15 pages, 10 figures

References in corpus (20)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Negative Specific Heat in Astronomy, Physics and Chemistry
• Inequivalence of ensembles in a system with long range interactions
• Breaking of ergodicity and long relaxation times in systems with long-range interactions
• Classification of phase transitions and ensemble inequivalence, 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
• On first-order phase transition in microcanonical and canonical non-extensive systems
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries
• Ensemble inequivalence in systems with long-range interactions
• Phase transition in a 2-dimensional Heisenberg model
• Eigenvalue Separation in Some Random Matrix Models
• Long-range correlations and ensemble inequivalence in a generalized ABC model
• Statistical Mechanics of systems with long range interactions
• Two-Dimensional Heisenberg Model with Nonlinear Interactions
• Phase diagram of the ABC model with nonconserving processes
• Ensemble Inequivalence and the Spin-Glass Transition
• Many-body spin glasses in the microcanonical ensemble
• Microcanonical Analysis of Spin Glasses Using Gauge Symmetry

Cited by in corpus (5)

• Macroscopic Length Correlations in Non-Equilibrium Systems and Their Possible Realizatons
• Ensemble inequivalence : Landau theory and the ABC model
• Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking
• Ensemble inequivalence and absence of quasi-stationary states in long-range random networks
• Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system