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Part of the book series: Mathematics and Its Applications (Soviet Series) ((MAIA,volume 61))

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Abstract

Random lattice models are reviewed. Different types of randomness are discussed. Different formulations of the statistical mechanics of quenched random systems are compared to each other. Theories of the critical behavior of random systems are compared to experimental results, mainly obtained for random ferromagnets. New theoretical results, obtained by the transfer tensor method, are presented, describing the non critical behavior.

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References

  1. R.B.Stinchcombe, in: Phase Transition and Critical Phenomena, vol.7, C.Domb and J.L.Lebowitz, eds. ( Academic Press, London, 1983 ).

    Google Scholar 

  2. Disordered Systems and Localisation, Lecture Notes in Physics 149, C.Castellani, C.Di Castro and L.Peliti, eds.(Springer, Berlin 1981 ).

    Google Scholar 

  3. Phase Transitions in Disordered Systems, Lecture Notes in Physics 206, A. Pekalski and J.Sznajd, eds. ( Springer, Berlin 1984 ).

    Google Scholar 

  4. see e.g. G.Toulouse, Com. Phys. 2(1977)115

    Google Scholar 

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

    Article  Google Scholar 

  6. R.Brout, Phys.Rev. 115(1959)824

    Article  MathSciNet  MATH  Google Scholar 

  7. G.Sobotta, Physica 123A(1984)253

    Google Scholar 

  8. R.M.Mazo, J.Chem.Phys. 39(1963)1224

    Article  Google Scholar 

  9. T.Morita, J.Math.Phys.5(1964)1401

    Article  Google Scholar 

  10. G.Sobotta and D.Wagner, Z.Phys. B33(1979)271;G.Sobotta in ref. 3

    Google Scholar 

  11. E.T.Jaynes, Phys.Rev. 106(1957)620,108(1957)171

    Google Scholar 

  12. D.N.Zubarev, Non-equilibrium Statistical Thermodynamics ( Plenum, London, 1974 ).

    Google Scholar 

  13. G.Sobotta and D.Wagner, J.Magn.Magn.Mat. 49(1985)77

    Article  Google Scholar 

  14. D.C.Rapaport, J.Phys. C5(1972)1830

    Article  Google Scholar 

  15. G.S.Rushbrooke,R.A.Muse,R.L.Stephenson and K.Pirnie, J.Phys. C5 (1972)3371

    Article  Google Scholar 

  16. D.P.Landau, Phys.Rev. B22(1980)2450

    Google Scholar 

  17. J.Marro, A.Labarta and J.Tejada, preprint (1985)

    Google Scholar 

  18. D.Chowdhury and D.Stauffer, preprint (1985)

    Google Scholar 

  19. G.Grinstein and A.Luther, Phys.Rev B13(1976)1329

    Google Scholar 

  20. T.C.Lubensky, Phys.Rev. B11(1975)11

    Article  Google Scholar 

  21. A.Sütö in ref. 3.

    Google Scholar 

  22. G.Sobotta and D.Wagner, J.Magn.Magn.Mat. 6(1977)92;

    Article  Google Scholar 

  23. G.Sobotta and D.Wagner, J.Phys. C11(1978)1467

    Google Scholar 

  24. G.Sobotta, J.Magn.Magn.Mat. 28(1982)1

    Article  Google Scholar 

  25. M.E.Fisher, Phys.Rev. 176(1968)275

    Google Scholar 

  26. A.B.Harris, J.Phys. C7(1974)1671

    Google Scholar 

  27. D.Stauffer, Phys.Rept. 54(1979)1;

    Article  Google Scholar 

  28. J.W.Essam, Rep.Prog.Phys. 43 (1980)833

    Article  MathSciNet  Google Scholar 

  29. H.O.Heuer and D.Wagner, J.Magn.Magn,Mat. 45(1984)272

    Article  Google Scholar 

  30. G.Herres, Diplomarbeit, Bochum (1983)

    Google Scholar 

  31. K.Westerholt and G.Sobotta, J.Phys. F13(1983)2371

    Article  Google Scholar 

  32. K.Westerholt and G.Sobotta in ref. 3 (see also ref. 46)

    Google Scholar 

  33. G.Sobotta and D.Wagner, J.Magn.Magn.Mat. 15–18(1980)257

    Google Scholar 

  34. G.Sobotta, Physica 129A(1985)343

    MathSciNet  Google Scholar 

  35. G.Sobotta, Physica 130A(1985)254

    Google Scholar 

  36. G.Sobotta, Physica 131A(1985)115

    MathSciNet  Google Scholar 

  37. G.Sobotta, Physica 132A(1985)457

    Google Scholar 

  38. G.Sobotta, Physica 136A(1986)475

    MathSciNet  Google Scholar 

  39. G.Sobotta, Physica 136A(1986) 487

    MathSciNet  Google Scholar 

  40. G.Sobotta, Physica 136A(1986) 495

    MathSciNet  Google Scholar 

  41. G.Sobotta, Physica 136A(1986) 525

    MathSciNet  Google Scholar 

  42. G.Sobotta, Physica 136A(1986) 537

    MathSciNet  Google Scholar 

  43. M.E.Fisher and J.W.Essam, J.Math.Phys. 2(1961)609

    Article  MathSciNet  MATH  Google Scholar 

  44. L.Onsager, Phys.Rev. 65(1944)117;

    Article  MathSciNet  MATH  Google Scholar 

  45. L.Onsager and B.Kaufmann, Phys.Rev. 76(1949)1232,1244

    Article  MATH  Google Scholar 

  46. M.F.Sykes, D.S.Gaunt and M.Glen, J.Phys. A9(1976)97

    Google Scholar 

  47. see e.g. B.Derrida and D.Stauffer, J.Physque 46(1985)1623

    Google Scholar 

  48. B.Hoeppener, G.Sobotta and D.Wagner, J.Phys. C12(1979)4553; see also ref. 1

    Google Scholar 

  49. J. Wosniza and H. v. Löhneysen, DPG Frühjahrstagung Münster 1989.

    Google Scholar 

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© 1990 Kluwer Academic Publishers

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Sobotta, G. (1990). Random Lattice Models. In: Albeverio, S., Streit, L., Blanchard, P. (eds) Stochastic Processes and their Applications. Mathematics and Its Applications (Soviet Series), vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2117-7_19

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  • DOI: https://doi.org/10.1007/978-94-009-2117-7_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7452-0

  • Online ISBN: 978-94-009-2117-7

  • eBook Packages: Springer Book Archive

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