Abstract
For classical lattice systems with finite-range interactions it is proven that if a state minimizes a free-energy functional at nonzero temperature with respect to variations of the state inside all regions of limited size (for instance, all regions with only one lattice site!) then it is a Gibbs state. This result rules out the possibility of defining metastable states atT ≠ 0 as those which satisfy the thermodynamical stability conditions for regions with small volume-to-surface ratio, unlike theT=0 case.
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References
R. L. Dobrushin,Theor. Prob. Appl. 13:201 (1968);Funct. Anal. Appl. 2:31 and 44 (1968); O. E. Lanford III and D. Ruelle,Commun. Math. Phys. 13:194 (1969).
O. Penrose and J. L. Lebowitz, Towards a rigorous molecular theory of metastability, inStudies in Statistical Mechanics, Vol. 7, E. W. Montroll and J. L. Lebowitz, eds. (North Holland, Amsterdam 1979), pp. 293–240.
G. L. Sewell, Stability, equilibrium and metastability in statistical mechanics,Phys. Rep. 57:307–342 (1980).
D. Capocaccia, M. Cassandro, and E. Olivieri,Commun. Math. Phys. 39:185 (1974).
F. Spitzer,Random Fields and Interacting Particle Systems, (Mathematical Association of America, Oberlin, Ohio 1971).
E. Presutti, Lectures notes in statistical mechanics, Universidade de São Paulo, 1979 (unpublished).
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Perez, J.F., Schonmann, R.H. On the global character of some restricted equilibrium conditions—A remark on metastability. J Stat Phys 28, 479–485 (1982). https://doi.org/10.1007/BF01008319
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DOI: https://doi.org/10.1007/BF01008319