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Book Review

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Full text of review: PDF
Book Information:

Author: C. M. Newman
Title: Topics in disordered systems
Additional book information: Birkhäuser-Verlag, Basel, 1997, vii + 88 pp., ISBN 3-7643-5777-0, $22.50

References [Enhancements On Off] (What's this?)

  • [BP] Anton Bovier and Pierre Picco (eds.), Mathematical aspects of spin glasses and neural networks, Progress in Probability, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1998. MR 1601723
  • [EA] S.F. Edwards and P.W. Anderson, Theory of spin glasses, J. Phys. F 5 (1975) 965-974.
  • [FHbk] K.H. Fisher and J.A. Hertz, Spin Glasses, Cambridge University Press, Cambridge, 1991.
  • [FH] D.S. Fisher and D.A. Huse, Ordered phase of short-range Ising spin glasses, Phys. Rev. Lett. 56 (1986) 1601-1604.
  • [FK] C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models, Physica 57 (1972), 536–564. MR 0359655
  • [Fr] Jürg Fröhlich, Mathematical aspects of the physics of disordered systems, Phénomènes critiques, systèmes aléatoires, théories de jauge, Part I, II (Les Houches, 1984) North-Holland, Amsterdam, 1986, pp. 725–893. With the collaboration of A. Bovier and U. Glaus. MR 880538
  • [Ge] Hans-Otto Georgii, Gibbs measures and phase transitions, de Gruyter Studies in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1988. MR 956646
  • [Ka] T. Kasuya, A theory of metallic ferro- and antiferromagnetism in Zener's model, Progr. Theoret. Phys. 16 (1956) 45-57.
  • [KS] J. Krug and H. Spohn, Kinetic roughening of growing surfaces, in Solids Far from Equilibrium: Growth, Morphology and Defects (C. Godrèche, ed.) 479-582, Cambridge University Press, Cambridge, 1991.
  • [LN] Cristina Licea and Charles M. Newman, Geodesics in two-dimensional first-passage percolation, Ann. Probab. 24 (1996), no. 1, 399–410. MR 1387641, 10.1214/aop/1042644722
  • [LNP] C. Licea, C. M. Newman, and M. S. T. Piza, Superdiffusivity in first-passage percolation, Probab. Theory Related Fields 106 (1996), no. 4, 559–591. MR 1421992, 10.1007/s004400050075
  • [Mc] W.L. McMillan, Scaling theory of Ising spin glasses, J. Phys. C 17 (1984) 3179-3187.
  • [MPV] Marc Mézard, Giorgio Parisi, and Miguel Angel Virasoro, Spin glass theory and beyond, World Scientific Lecture Notes in Physics, vol. 9, World Scientific Publishing Co., Inc., Teaneck, NJ, 1987. MR 1026102
  • [My] J.A. Mydosh, Spin Glasses: An Experimental Introduction, Taylor and Francis, London, 1993.
  • [Ne] Charles M. Newman, Disordered Ising systems and random cluster representations, Probability and phase transition (Cambridge, 1993) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 420, Kluwer Acad. Publ., Dordrecht, 1994, pp. 247–260. MR 1283186, 10.1007/978-94-015-8326-8_15
  • [NS92] C.M. Newman and D.L. Stein, Multiple states and thermodynamic limits in short ranged spin glass models, Phys. Rev. B 46 (1992) 973-982.
  • [NS96a] C. M. Newman and D. L. Stein, Ground-state structure in a highly disordered spin-glass model, J. Statist. Phys. 82 (1996), no. 3-4, 1113–1132. MR 1372437, 10.1007/BF02179805
  • [NS96b] C.M. Newman and D.L. Stein, Non-mean-field behavior of realistic spin glass, Phys. Rev. Lett. 76 (1996) 515-518.
  • [NS96c] C.M. Newman and D.L. Stein, Spatial inhomogeneity and thermodynamic chaos, Phys. Rev. Lett. 76 (1996) 4821-4824.
  • [Pa] G. Parisi, Infinite number of order parameters for spin-glasses, Phys. Rev. Lett. 43 (1979) 1754-1756.
  • [RK] M.A. Ruderman and C. Kittel, Indirect exchange coupling of nuclear magnetic moments by conduction electrons, Phys. Rev. 96 (1954) 99-102.
  • [SK] D. Sherrington and S. Kirkpatrick, Solvable model of a spin glass, Phys. Rev. Lett. 35 (1975) 1792-1796.
  • [Si] Barry Simon, The statistical mechanics of lattice gases. Vol. I, Princeton Series in Physics, Princeton University Press, Princeton, NJ, 1993. MR 1239893
  • [We] Jan Wehr, On the number of infinite geodesics and ground states in disordered systems, J. Statist. Phys. 87 (1997), no. 1-2, 439–447. MR 1453745, 10.1007/BF02181495
  • [Yo] K. Yosida, Magnetic properties of Cu-Mn alloys, Phys. Rev. 106 (1957) 893-898.

Review Information:

Reviewer: Kenneth S. Alexander
Affiliation: University of Southern California, Los Angeles
Email: alexandr@math.usc.edu
Journal: Bull. Amer. Math. Soc. 36 (1999), 267-270
DOI: https://doi.org/10.1090/S0273-0979-99-00779-X
Keywords: Disordered system, spin glass, Ising model, random cluster model
Published electronically: February 22, 1999
Additional Notes: Research supported by NSF grant DMS-9802368.
Review copyright: © Copyright 1999 American Mathematical Society