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Renormalization and scaling of a two-dimensional Ising system in a transverse field at Tc>0

Author

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  • Stella, A.L.
  • Toigo, F.

Abstract

A quantum generalization of the Niemeijer and van Leeuwen (N-vL) renormalization group transformation is constructed which allows to study the critical properties (at Tc>0) of a two-dimensional Ising system with a transverse field on a triangular lattice. Explicit calculations are performed in a second order cumulant expansion. Only one fixed point is found corresponding to the same Ising-like hamiltonian given by N-vl. The linearized transformation has a zero eigenvalue associated with Γ, the transverse field strength. The critical properties of the system are briefly discussed; in particular we show that the singular behaviour of the transverse susceptibility at Γ = 0, which turns out to be of the same kind as that of the energy density, is explained by the existence of such a zero eigenvalue. Our arguments suggest a natural extension of this result to three dimensions.

Suggested Citation

  • Stella, A.L. & Toigo, F., 1977. "Renormalization and scaling of a two-dimensional Ising system in a transverse field at Tc>0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(1), pages 175-190.
    • Handle: RePEc:eee:phsmap:v:89:y:1977:i:1:p:175-190
    DOI: 10.1016/0378-4371(77)90148-0
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    References listed on IDEAS

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    1. Dekeyser, R. & Reynaert, M., 1976. "The XY-model and the self-avoiding walk approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(1), pages 197-204.
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    Cited by:

    1. Van Wonderen, A.J. & Suttorp, L.G., 1987. "Equilibrium properties of a multi-component ionic mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 145(3), pages 557-583.
    2. del Río, Fernando & Benavides, Ana Laura & Guevara, Yolanda, 1995. "Vapor-liquid equilibrium of a multipolar square-well fluid II. Effect of a variable square-well range," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(1), pages 10-20.
    3. Suttorp, L.G. & Van Wonderen, A.J., 1987. "Equilibrium properties of a multi-component ionic mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 145(3), pages 533-556.
    4. Konior, J. & Jȩdrzejek, C., 1989. "Mean spherical approximation equations for a symmetric hard-core two-yukawa mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 161(2), pages 339-356.

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