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On the thermodynamics of the random one-dimensional Ising chain in a transverse field

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  • Braeter, H.
  • Kowalski, J.M.

Abstract

For three simple one-dimensional disordered models: (a) the Ising chain with random magnetic moments in a transverse field, (b) the Ising chain with random coupling constants in a transverse field, and (c) the X-Y model with a special type of disorder, the asymptotic equivalence in the thermodynamic limit is proved and some of its consequences are discussed. The spectral density of the finite chain for the model (a) is calculated by Dean's method for several representative cases and the presence of the local modes is indicated. The expressions for the initial susceptibilities for the models (a) and (b) are reviewed and (in two cases) the derivations are simplified.

Suggested Citation

  • Braeter, H. & Kowalski, J.M., 1977. "On the thermodynamics of the random one-dimensional Ising chain in a transverse field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(2), pages 243-257.
    • Handle: RePEc:eee:phsmap:v:87:y:1977:i:2:p:243-257
    DOI: 10.1016/0378-4371(77)90015-2
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    References listed on IDEAS

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    1. van Hemmen, J.L. & Vertogen, G., 1975. "A note on Fermi lattice systems with bilinear hamiltonians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(3), pages 391-410.
    2. Lebowitz, Michael A., 1968. "Canada's First Bank: A History of the Bank of Montreal. By Merrill Denison. Two Volumes. New York: Dodd, Mead & Co., 1966, 1967. Pp. xix, 472; xiii, 454. $7.50 each," The Journal of Economic History, Cambridge University Press, vol. 28(4), pages 660-661, December.
    3. Huiskamp, W.J., 1975. "Editorial," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 79(1), pages 1-1.
    4. Siskens, Th.J. & Capel, H.W. & Gaemers, K.J.F., 1975. "On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 79(3), pages 259-295.
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    Cited by:

    1. Perk, J.H.H. & Capel, H.W., 1978. "Transverse correlations in the inhomogeneous one-dimensional XY-model at infinite temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(1), pages 163-184.
    2. Perk, J.H.H. & Capel, H.W. & Siskens, Th.J., 1977. "Time correlation functions and ergodic properties in the alternating XY-chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(2), pages 304-325.
    3. Capel, H.W. & Perk, J.H.H., 1977. "Autocorrelation function of the x-component of the magnetization in the one-dimensional XY-model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(2), pages 211-242.
    4. Perk, J.H.H. & Capel, H.W., 1977. "Time-dependent xx-correlation functions in the one-dimensional XY-model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(2), pages 265-303.

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