Abstract
We study the low-temperature phase of the nearest-neighbor Ising spin glass. Our analysis of gauge-invariant ground state Peierls contours suggests the existence of infinitely many disjoint Gibbs states at low temperatures, provided the dimension,d, is sufficiently large (presumablyd> 3 or 4), while ford=2 the Gibbs state is unique for all temperatures. Ind ⩾ 3 we present arguments supporting the existence of a massless phase with broken spin-flip symmetry at low temperatures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. W. Anderson, Survey of theories of spin glasses, inAmorphous Magnetism II, R. A. Levy and R. Hasegawa, eds. (Plenum Press, New York, 1977).
G. Toulouse, Frustration and disorder in statistical mechanics: spin glasses in historical perspective, inHeidelberg Colloquium on Spin Glasses, J. L. van Hemmen and I. Morgenstern, eds. (Springer Verlag, Berlin, Heidelberg, New York, Tokyo 1983), and other papers in this volume.
K. H. Fischer,Phys. Status Solidi (b) 116:357 (1983).
R. N. Bhatt and A. P. Young,Phys. Rev. Lett. 54:340 (1985); A. T. Ogielski and I. Morgenstern,Phys. Rev. Lett. 54:428 (1985).
N. Sourlas,J. Phys. Lett. 45:L969 (1984).
S. Kirkpatrick and P. Sherrington,Phys. Rev. B17:4384 (1978).
G. Parisi,J. Phys. A13:1101 (1980);A13:1887 (1980)Phys. Rev. Lett. 50:1946 (1983).
M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro,Phys. Rev. Lett. 52:1156 (1984);J. Phys. 45:843 (1984).
V. Cannella and J. A. Mydosh,Phys. Rev. B6:4220 (1972).
P. W. Anderson, Princeton University preprint, 1985, and references therein.
S. F. Edwards and P. W. Anderson,J. Phys. F5:1965 (1975).
G. Toulouse,Commun. Phys. 2:115 (1977).
J. Fröhlich, Mathematical Aspects of the Physics of Disordered Systems, inProc. of the 1984 Les Houches Summer School, K. Osterwalder and R. Stora, eds. (Plenum Press, New York), 1986, to appear.
J. E. Avron, G. Röpstorff, and L. S. Schulman,J. Stat. Phys. 26:25 (1981).
D. C. Mattis,Phys. Lett. A50:421 (1976).
H. E. Kesten,Percolation Theory for Mathematicians, (Birkhäuser Verlag, Boston, Basel, Stuttgart, 1983); J. W. Essam, Percolation and cluster size, inPhase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic Press, London, 1972).
M. Aizenman and E. Lieb,J. Stat. Phys. 24:279 (1981).
S. A. Pirogov and Ya. G. Sinai,Teor. Mat. Fiz. 25:358 (1975) [Theor. Math. Phys. 25: 1185 (1976);Teor. Mat. Fiz. 26:61 (1976) [Theor. Math. Phys. 26:39 (1976)].
J. Slawny,J. Stat. Phys. 20:711 (1979); M. Zahradnik,Commun. Math. Phys. 93:559 (1984).
M. E. Fisher,J. Appl. Phys. 38:981 (1967); N. D. Mermin,J. Phys. Soc. Jpn. Suppl. 26:263 (1969).
R. Peierls,Proc. Cambridge Philos. Soc. 32:477 (1936); R. Griffiths,Phys. Rev. 136:A437 (1964).
F. J. Dyson,Commun. Math. Phys. 12:91, 212 (1969).
J. Fröhlich and T. Spencer,Commun. Math. Phys. 81:527 (1981).
Ch.-E. Pfister,Commun. Math. Phys. 79:181 (1981).
R. L. Dobrushin,Theor. Prob. Appl. 73:582 (1972).
M. Aizenman,Commun. Math. Phys. 73:83 (1980).
J. Vannimenus and G. Toulouse,J. Phys. C10:L537 (1977); S. Kirkpatrick,Phys. Rev. B16:4630 (1977); I. Morgenstern and K. Binder,Phys. Rev. B22:288 (1980).
B. Derrida,Phys. Rev. B24:2613 (1981).
D. A. Huse and Ch. L. Henley,Phys. Rev. Lett. 54:2704 (1985); M. Kardar,Phys. Rev. Lett. 55:2923 (1985); A. Bovier, J. Fröhlich, and U. Glaus,Phys. Rev. B (1986), to appear.
J. Villain,Phys. Rev. Lett. 52:1543 (1984); inScaling Phenomena in Disordered Systems, R. Rhynn, ed., (1986, to appear); R. Bruinsma and G. Aeppli,Phys. Rev. Lett. 52:1547 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bovier, A., Fröhlich, J. A heuristic theory of the spin glass phase. J Stat Phys 44, 347–391 (1986). https://doi.org/10.1007/BF01011303
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01011303