Tropical Limit in Statistical Physics
arXiv:1502.01229 · doi:10.1016/j.physleta.2015.04.003
Abstract
Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adapted to analyse properties of systems with highly degenerated energy levels, particularly of frustrated systems like spin ice and spin glasses. Tropical free energy is a piecewise linear function of temperature, tropical entropy is a piecewise constant function and the system has energy for which tropical Gibbs' probability has maximum. Properties of systems in the points of jump of entropy are studied. Systems with finite and infinitely many energy levels and phenomena of limiting temperatures are discussed.
16 pages, 6 figures
References in corpus (10)
- Spin Ice State in Frustrated Magnetic Pyrochlore Materials
- Ising models of quantum frustration
- Tropical Geometry of Statistical Models
- The A^{(1)}_M automata related to crystals of symmetric tensors
- Zero Point Entropy in Stuffed Spin Ice
- Correspondence principle for idempotent calculus and some computer applications
- Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- KP line solitons and Tamari lattices
- Thermodynamics and the moment map
- Where is the residual entropy of a glass hiding?
Cited by in corpus (8)
- Tropical limit and the micro-macro correspondence
- Geometry of the basic statistical physics mapping
- Entropy driven transformations of statistical hypersurfaces
- Signatures of partition functions and their complexity reduction through the KP II equation
- Tropical Limit for Configurational Geometry in Discrete Thermodynamic Systems
- Integrability properties and multi-kink solutions of a generalised Fokker-Planck equation
- Some statistics about Tropical Sandpile Model
- Zeros and amoebas of partition functions