Book Review
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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,
$22.50$
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.
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 359655
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
Hans-Otto Georgii, Gibbs measures and phase transitions, De Gruyter Studies in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1988. MR 956646, DOI 10.1515/9783110850147
[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.
Cristina Licea and Charles M. Newman, Geodesics in two-dimensional first-passage percolation, Ann. Probab. 24 (1996), no. 1, 399–410. MR 1387641, DOI 10.1214/aop/1042644722
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, DOI 10.1007/s004400050075
[Mc] W.L. McMillan, Scaling theory of Ising spin glasses, J. Phys. C 17 (1984) 3179-3187.
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.
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, DOI 10.1007/978-94-015-8326-8_{1}5
[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.
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, DOI 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.
Barry Simon, The statistical mechanics of lattice gases. Vol. I, Princeton Series in Physics, Princeton University Press, Princeton, NJ, 1993. MR 1239893, DOI 10.1515/9781400863433
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, DOI 10.1007/BF02181495
[Yo] K. Yosida, Magnetic properties of Cu-Mn alloys, Phys. Rev. 106 (1957) 893-898.
- [BP]
- A. Bovier and P. Picco, eds., Mathematical Aspects of Spin Glasses and Neural Networks, Progress in Probability Volume 41, Birkhäuser, Boston, 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, Phys. 57 (1972) 536-564. MR 0359655
- [Fr]
- J. Fröhlich, Mathematical aspects of the theory of disordered systems, in Critical Phenomena, Random Systems and Gauge Theories, Les Houches Session XLIII 1984 (K. Osterwalder and R. Stora, eds.) 725-893, North-Holland, Amsterdam, 1986. MR 0880538
- [Ge]
- H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, Berlin, 1988. MR 0956646
- [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]
- C. Licea and C.M. Newman, Geodesics in two-dimensional first-passage percolation, Ann. Probab. 24 (1996) 399-410. MR 1387641
- [LNP]
- C. Licea, C.M. Newman and M.S.T. Piza, Superdiffusivity in first-passage percolation, Prob. Theory Related Fields 106 (1996) 559-591. MR 1421992
- [Mc]
- W.L. McMillan, Scaling theory of Ising spin glasses, J. Phys. C 17 (1984) 3179-3187.
- [MPV]
- M. Mézard, G. Parisi and M.A. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore, 1987. MR 1026102
- [My]
- J.A. Mydosh, Spin Glasses: An Experimental Introduction, Taylor and Francis, London, 1993.
- [Ne]
- C.M. Newman, Disordered Ising systems and random cluster representation, in Probability and Phase Transition (G. Grimmett, ed.), 247-260, Kluwer, Dordrecht, 1994. MR 1283186
- [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) 1113-1132. MR 1372437
- [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]
- B. Simon, The Statistical Mechanics of Lattice Gases, Vol. 1, Princeton University Press, Princeton, 1993. MR 1239893
- [We]
- J. Wehr, On the number of infinite geodesics and ground states in disordered systems, J. Statist. Phys. 87 (1997) 439-447. MR 1453745
- [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
