On a classical spin glass model

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Morgenstern, I., Horner, H.: Phys. Rev. B25, 504 (1982)

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Penrose, O., Lebowitz, J.L.: In: Fluctuation phenomena. Montroll, E.W., Lebowitz, J.L. (eds), Chap. 5. Amsterdam: North-Holland 1979

Sewell, G.L.: Phys. Rep.57, 307 (1980)

Sherrington, D., Kirkpatrick, S.: Phys. Rev. Lett.35, 1792 (1975) referred to as SK

Kirkpatrick, S., Sherrington, D.: Phys. Rev. B17, 4384 (1978)

Thouless, D.J., Anderson, P.W., Palmer, R.G.: Philos. Mag.35, 593 (1977) referred to as TAP

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Sommers, H.J.: Z. Phys. B-Condensed Matter31, 301 (1978);33, 173 (1979)

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Gabay, M.: Ph.D. Thesis, Orsay 1981

Sompolinsky, H.: Phys. Rev. Lett.47, 935 (1981)

For a review see G. Toulouse, ?Frustrations et désordres: problèmes nouveaux en mécanique statistique. Histoire des verres de spin?, Meeting, Clermont-Ferrand (1981) J. Phys. (Paris) (to be published)

Toulouse, G.: Commun. Phys.2, 115 (1977)

Kirkpatrick, S.: Phys. Rev. B16, 4630 (1977)

Binder, K., Schröder, K.: Phys. Rev. B14, 2142 (1976) in part. their Fig. 1

Springer, M.D.: The algebra of random variables. New York: Wiley 1979

Lamperti, J.: Probability. Sect. 14. New York: Benjamin 1966

Luttinger, J.M.: Phys. Rev. Lett.37, 778 (1976)

Kubo, R.: J. Phys. Soc. Jpn.17, 1100 (1962)

Anderson, P.W.: Rev. Mod. Phys.50, 199 (1978)

Huang, K.: Statistical mechanics. Sect. 8.2. New York: Wiley 1963

Bruijn, N.G. de: Asymptotic methods in analysis. 2nd Edn., Sect. 4.2. Amsterdam: North-Holland 1961

Using the strong law of large numbers (Ref. 23, Sect. 7) or the ergodic theorem

Cramér, H.: Act. Sci. Ind., Vol. 736, pp. 5?23. Paris: Hermann 1938

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Roberts, A.W., Varberg, D.E.: Convex functions, pp. 30 and 110. New York: Academic Press 1973

Varadhan, S.R.S.: Commun. Pure Appl. Math.19, 261 (1966) in part. Theorem 3.4

Kac, M.: In: Statistical physics, phase transitions and superfluidity. Chrétien, M., Gross, E.P., Deser, S. (eds.), Vol. 1, pp. 248?249. New York: Gordon and Breach 1968. See also Stanley, H.E.: Introduction to phase transitions and critical phenomena. Sect. 6.5. Oxford: Oxford University Press 1971

Donsker, M.D., Varadhan, S.R.S.: Phys. Rep.77, 235 (1981) and references quoted therein. Additional information may be found in Ref.32. See also R.S. Ellis, Large deviations and other limit theorems for a class of dependent random variables with applications to statistical mechanics, Z. Wahrscheinlichkeitstheorie (submitted for publication)

Ref. 22, Sect. 15

Bray, A.J., Moore, M.A.: J. Phys. C13, L469 (1980)

Young, A.P.: J. Phys. C14, L 1085 (1981)

Mattis, D.C.: Phys. Lett.56 A, 421 (1976)

If one scales by 1/2N instead ofN and replacesK by ?J 0 one just gets (3.13). Hence the transition atK=1; it is second order

Scaling by 1/2N instead ofN in theJ 0-term leaves us with an extra factor 1/2 so that the ferromagnetic transition itself would occur at 1/2?J 0=1. Note this transition is second order too

Schulze, U., Felten, G., Schwink, Ch.: J. Magn. Magn. Mater.15?18, 205 (1980) in part. Fig. 1

Crane, S., Claus, H.: Phys. Rev. Lett.46, 1693 (1981)

Landau, L.D., Lifshitz, E.M.: Statistical physics. 2nd. Edn., pp. 478?479. Oxford: Pergamon Press 1969

Simon, B., Sokal, A.D.: J. Stat. Phys.25, 679 (1981)

Ref. 31, Theorem 15.D and problem 43.D

Fenchel, W.: Can. J. Math.1, 73 (1949)

Eisele, Th., Ellis, R.S.: Symmetry breaking and random waves for magnetic systems on a circle. Preprint, Heidelberg, 1981, Appendix C

See also a recent discussion in Phys. Rev. Lett.: Gullikson, E.M., Schultz, S.: Phys. Rev. Lett.49, 238 (1982)

Wenger, L.E., Mydosh, J.A.: ibid.49, p. 239 (1982)

Fogle, W.E., Boyer, J.D., Phillips, N.E., Curen, J. Van: ibid.49, p. 241 (1982)

Larsen, U.: Phys. Rev. B18, 5014 (1978)

Ref. 31??, 110, and 115 New York: Academic Press 1973

Ref. 31?? and Theorem 51.E New York: Academic Press 1973

Chung, K.L.: Elementary probability theory with stochastic processes. 2nd Edn., Sect. 7.3. Berlin, Heidelberg, New York: Springer-Verlag 1975

Feller, W.: An introduction to probability theory and its applications. Vol. I, 3rd Edn., Sect. VII.3. New York: Wiley 1970

Ref. 31??, Theorem 42.F New York: Academic Press 1973

Iooss, G., Joseph, D.D.: Elementary stability and bifurcation theory. Berlin, Heidelberg, New York: Springer-Verlag 1980

Eisele, Th., Enter, A.C.D. van, Hemmen, J.L. van: (Manuscript in preparation)

See, for instance, Verbeek, B.H., Nieuwenhuys, G.J., Stocker, H., Mydosh, J.A.: Phys. Rev. Lett.40, 586 (1978)

Shell, J., Cowen, J.A., Foiles, C.L.: Phys. Rev. B25, 6015 (1982)

Anderson, P.W., Halperin, B.I., Varma, C.M.: Philos. Mag.25, 1 (1972)

Wenger, L.E., Keesom, P.H.: Phys. Rev. B13, 4053 (1976)

See also Joffrin, J.: In: Ill-condensed matter, Les Houches 1978. Balian, R., Maynard, R., Toulouse, G. (eds.), Sects. 1.1 and 1.2. Amsterdam: North-Holland 1979

Binder, K.: In: Fundamental problems in statistical mechanics. Cohen, E.G.D. (ed.), Vol. V, pp. 21?51. Amsterdam: North-Holland 1980

Soukoulis, C.M., Levin, K., Grest, G.S.: Phys. Rev. Lett.48, 1756 (1982)