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Renormalization group and quantum critical phenomena in the large-n limit

Author

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  • Busiello, G.
  • De Cesare, L.
  • Rabuffo, I.

Abstract

The paper is devoted to a sistematic study of the critical behaviour and quantum regime of a wide class of quantum systems on the basis of the Renormalization Group (RG) approach in the large-n limit. It can be considered as a complement to recent perturbative (RG) investigations for the same systems and as a convenient basis for a treatment of the classical-quantum crossover. The differences between “Bosonized systems” and several quantum systems for which a dimensional crossover occurs in the low temperature limit are emphasized, consistently with the perturbative results and a calculation of the quantum non linear scaling field is also realized. Finally, a differential formulation of the quantum RG in the large-n limit is presented and its convenience in investigating some aspects of the problem is pointed out.

Suggested Citation

  • Busiello, G. & De Cesare, L. & Rabuffo, I., 1983. "Renormalization group and quantum critical phenomena in the large-n limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(2), pages 445-481.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:2:p:445-481
    DOI: 10.1016/0378-4371(83)90126-7
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    Citations

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    Cited by:

    1. Plakida, N.M. & Tonchev, N.S., 1986. "Quantum effects in a d-dimensional exactly solvable model for a structural phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(1), pages 176-188.
    2. Tonchev, N.S., 1988. "Finite-size effects in a quantum exactly soluble model for structural phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(1), pages 356-360.
    3. Busiello, G. & De Cesare, L. & Rabuffo, I., 1987. "Destruction of long-range order in quantum ferroelectrics via random field fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(1), pages 192-200.
    4. Korutcheva, E.R. & Tonchev, N.S., 1993. "On the quantum finite-size sealing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 195(1), pages 215-222.
    5. Lukierska-Walasek, K., 1984. "Quantum crossover behaviour of the X−Y model in a transverse magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(3), pages 613-626.
    6. Tonchev, N.S., 1991. "On the finite-size scaling in quantum critical phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(2), pages 374-383.
    7. Uzunov, D.I. & Korutcheva, E.R. & Millev, Y.T., 1985. "Random field effects in classical and quantum critical phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(3), pages 535-549.

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