Abstract
The entropyS T (j) of a two-dimensional Ising spin glass with an independent distribution of the random couplingp(J)=x·δ(J+1)+(1-x)δ(J-j) is discontinuous for temperatureT=0 and rationalj>0 and continuous elsewhere. The integrated density of frequenciesk M (ω 2) of an one-dimensional chain of coupled oscillators with an independent distribution of the random massesp(m)=x·δ(m-1)+(1-x)δ(m-M) has the same behaviour, whereω 2 corresponds toj andM to 1/T. The discontinuity points for infiniteM are, for sufficiently large but finiteM, special, frequencies, wherek M (ω 2) has a Lifshitz singularity.
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References
Bentosela, F., Carmona, R., Duclos, P., Simon, B., Souillard, B., Weder, R.: Commun. Math. Phys.88, 387 (1983)
Simon, B.: Adv. Appl. Math.3, 463 (1982)
Aubry, S.: In: Seminar on the Riemann problem, spectral theory and complete integrability 1978/79. Chudnovsky, D.G., (ed.). Berlin, Heidelberg, New York: Springer-Verlag 1980
Avron, J., Simon, B.: Duke Math. J.50, 369 (1983)
Hori, J.: Spectral properties of disordered chains and lattices. Oxford: Pergamon Press 1968
Leib, E.H., Mattis, D.C.: Mathematical physics in one dimension. New York: Academic Press 1966
Endrullis, M., Englisch, H.: Special frequencies and special energies. Preprint (in preparation)
Endrullis, M.: Two-dimensional spin glasses with variable couplings. Preprint (in preparation)
Avron, J.E., Roepstorff, G., Schulman, L.S.: J. Stat. Phys.26, 25 (1981)
Aizenman, M., Lieb, E.H.: J. Stat. Phys.24, 279 (1981)
Ruelle, D.: Statistical mechanics. New York: W.A. Benjamin 1969
Akcoglu, M.A., Krengel, U.: J. Reine und Angew. Math.323, 53 (1981)
Kirkpatrick, S.: Phys. Rev. B16, 4630 (1977)
Matsuda, H.: Prog. Theor. Phys.32, 161 (1964)
Ishii, K.: Suppl. Prog. Theor. Phys.53, 77 (1973)
Pastur, L.A.: Commun. Math. Phys.75, 179 (1980)
Englisch, H.: One-dimensional Schrödinger operators with ergodic potential. Z. Analysis Anwendung (to appear)
Hori, J.: Suppl Prog. Theor. Phys.36, 3 (1966)
Wada, K.: Prog. Theor. Phys.36, 726 (1966)
Kirsch, W., Martinelli, F.: J. Phys. A15, 2139 (1982)
Dean, P.: Prog. Theor. Phys.254, 507 (1960)
Matsuda, H., Okada, K.: Prog. Theor. Phys.34, 539 (1965)
Gredescul, S.A., Pastur, L.A.: Teor. Math. Fiz.23, 132 (1975)
Gubarnatis, J.E., Taylor, P.L.: J. Phys. C4, L92 (1971)
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Englisch, H. Discontinuities in disordered systems. Z. Physik B - Condensed Matter 53, 289–293 (1983). https://doi.org/10.1007/BF01436291
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DOI: https://doi.org/10.1007/BF01436291