Journal of Statistical Physics

, Volume 24, Issue 1, pp 279–297

The third law of thermodynamics and the degeneracy of the ground state for lattice systems

  • Michael Aizenman
  • Elliott H. Lieb

DOI: 10.1007/BF01007649

Cite this article as:
Aizenman, M. & Lieb, E.H. J Stat Phys (1981) 24: 279. doi:10.1007/BF01007649


The third law of thermodynamics, in the sense that the entropy per unit volume goes to zero as the temperature goes to zero, is investigated within the framework of statistical mechanics for quantum and classical lattice models. We present two main results: (i) For all models the question of whether the third law is satisfied can be decided completely in terms of ground-state degeneracies alone, provided these are computed for all possible “boundary conditions.” In principle, there is no need to investigate possible entropy contributions from low-lying excited states, (ii) The third law is shown to hold for ferromagnetic models by an analysis of the ground states.

Key words

Third law entropy thermodynamics lattice systems statistical mechanics 

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Michael Aizenman
    • 1
  • Elliott H. Lieb
    • 1
    • 2
  1. 1.Department of PhysicsPrinceton UniversityPrinceton
  2. 2.Department of MathematicsPrinceton UniversityPrinceton

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