Abstract
In this chapter we will use the general Lyapunov functionals introduced in Chapter 5 to study and describe the thermodynamic limit of Gibbs ensembles in Bethe lattice L ∞.
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References
Baxter, R.J., Exactly Solved Models in Statistical Mechanics, Academic Press, 1982.
Brascamp, H.J., Equilibrium States for a One Dimensional Lattice Gas, Comm. Math. Phys, 21, 1971, 56–70.
Fannes, M., A. Verbeure, On Solvable Models in Classical Lattice Systems, Comm. Math. Phys. 96, 1984, 115–124.
Goles, E., S. Martinez, The One-Site Distributions of Gibbs States on Bethe Lattice are Probability Vectors of Period ≤ 2 for a Nonlinear Transformation, J. Stat. Phys. 52, 1988, 267–285.
Krasnoselsky, M.A., Y.B. Rutitsky, Convex Functions and Orlicz Spaces, Industan Publ. Co., 1962.
Martínez, S., Lyapunov Functionals on Beth Lattice, in Proceedings Workshop on Disordered Systems, Bogotá,. World Sc. Publ. 1989, 22–37.
Martínez, S., Cylinder Distribution of Thermodynamic Limit of Beth e Lattice, Instabilities and Non-Equilibrium Structures II; Mathematics and Its Applications, Kluwer, 1989, 117–130.
Ruelle, D.,Thermodynamic Formalism, Addison-Wesley, 1978.
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© 1990 Kluwer Academic Publishers
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Goles, E., Martínez, S. (1990). Applications on Thermodynamic Limits on the Bethe Lattice. In: Neural and Automata Networks. Mathematics and Its Applications, vol 58. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0529-0_7
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DOI: https://doi.org/10.1007/978-94-009-0529-0_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6724-9
Online ISBN: 978-94-009-0529-0
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