Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions

DOI10.1088/1751-8113/48/14/145001zbMATH Open1327.82033arXiv1410.1279OpenAlexW3105204002MaRDI QIDQ5247141

Takashi Mori

Publication date: 23 April 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1410.1279

zbMATH Keywords

thermodynamic limitvariational methodsHamiltonian systemsentropy densityperiodic boundary conditionsfree boundary conditionsadditivitylong-range interactioncoarse-graininglattice spin systemscritical mean-field phenomenamean-field theory violation

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Classical equilibrium statistical mechanics (general) (82B05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Statistical thermodynamics (82B30)

Related Items (1)

Lattice gas models with long range interactions

This page was built for publication: Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions