Abstract
A new method, that systematically combines results of random matrix theory and the usual statistical mechanics, is described to study thermodynamic properties of disordered systems. Two exactly solvable models are examined in this formulation to illustrate the usefulness of this method for systems described by random as well as non-random Hamiltonian.
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References
Balian R, Maynard R and Toulouse G (eds) 1978Ill-condensed matter Les Houches Session XXXI (Amsterdam: North Holland)
Bohigas O and Flores J 1971Phys. Lett. B34 261
Brody T Aet al 1981Rev. Mod. Phys. 53 385
Cramer H 1946Mathematical methods of statistics (Princeton: University Press)
Dyson F J 1970Commun. Math. Phys. 19 235
French J B and Wong S S M 1970Phys. Lett. B33 449
French J B and Chang F S 1972 inStatistical properties of nuclei, (ed) J B Garg (New York: Plenum Press)
Kac M 1968 inStatistical physics, phase transitions and superfluidity (eds.) M Chretien, E P Gross and D Deser (New York: Gordon and Breach) Vol. 1
Khinchin A I 1949Mathematical foundations of statistical mechanics (New York: Dover)
Kosterlitzet al 1976Phys. Rev. Lett. 36 1217
Mehta M L 1967Random matrices and the statistical theory of energy levels (New York: Academic Press)
Mehta M L 1971Commun. Math. Phys. 20 245
Mon K K and French J B 1975Ann. Phys. 95 90
Porter C E (ed) 1965Statistical theories of spectra: fluctuations (New York: Academic Press)
Stanley H E 1971Introduction to phase transition and critical phenomena (Oxford: Clarendon Press)
Ziman J 1979Models of disorder (Cambridge: University Press)
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Parikh, J.C. Random matrix theory and the statistical mechanics of disordered systems. Pramana - J Phys 20, 467–476 (1983). https://doi.org/10.1007/BF02846282
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DOI: https://doi.org/10.1007/BF02846282