Abstract
We study the plane rotator model with Hamiltonian \(- \frac{1}{2}\sum\limits_{x \ne y} {\frac{{Jxy\cos (\mathcal{O}_x - \mathcal{O}_y )}}{{\left| {x - y} \right|^{3 + \mathcal{E}} }}}\)where Jxy for different pair (x.y) are independent symmetric unbounded random variables. It is proved that for almost all J, all Gibbs states P(J) are invariant by rotation.
Keywords
- Long Range
- Spin Glass
- Relative Entropy
- Gibbs State
- Borel Cantelli Lemma
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References
S.F. EDWARDS and P.W. ANDERSON, J. Phys. F 5, 965 (1975).
A.C.D. VAN ENTER and R.B. GRIFFITHS, Comm.Math.Phys. 90, 319 (1983).
P.A. VUILLERMOT, J. Phys. A10, 1319 (1977).
K.M. KHANIN and Ya. G. SINAI, J. Stat. Phys. 20, 573 (1979).
A.C.D. VAN ENTER and J.L. VAN HEMMEN, J. Stat. Phys. 32, 141 (1983).
K.M. KHANIN, Theoretich i Matem Fiz., 43, 253 (1980).
M. CASSANDRO, E. OLIVIERI, B. TIROZZI, Comm.Math.Phys. 87, 229 (1982).
P. PICCO, J. Stat. Phys. 32, 627 (1983).
P. PICCO, Upper bound on the decay of correlations in the plane rotator model with long range random interaction, Preprint Marseille (1982).
C. PFISTER, Comm.Math.Phys. 79, 181 (1981).
C. PFISTER and J. FROHLICH, Comm.Math.Phys. 81, 277 (1981).
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© 1985 Springer-Verlag
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Picco, P. (1985). On the absence of breakdown of symmetry for the plane rotator model with long range unbounded random interaction. In: Albeverio, S., Combe, P., Sirugue-Collin, M. (eds) Stochastic Aspects of Classical and Quantum Systems. Lecture Notes in Mathematics, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101542
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DOI: https://doi.org/10.1007/BFb0101542
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