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Quantum effects in a d-dimensional exactly solvable model for a structural phase transition

Author

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  • Plakida, N.M.
  • Tonchev, N.S.

Abstract

An exactly solvable d-dimensional model of a structural phase transition with a long-range anharmonic interaction is considered in the low temperature region Tc→0 when the quantum effects are essential. It is shown that the quantum fluctuations lead to a suppression of the phase transition. However, at Tc > 0 they do not change the critical behaviour. The latter becomes pure quantum mechanical at Tc=0 when the dimensional crossover is fulfilled, according to which the critical behaviour of a d-dimensional quantum system (Tc=0) and of a (d+1)-dimensional classical system (Tc<) becomes equivalent.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:136:y:1986:i:1:p:176-188
    DOI: 10.1016/0378-4371(86)90049-X
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    References listed on IDEAS

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    1. Tonchev, N.S. & Uzunov, D.I., 1985. "On the tricritical Lifshitz behaviour," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(1), pages 265-273.
    2. 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.
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    Citations

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    Cited by:

    1. Radosz, Andrzej, 1990. "Soft mode in the class of exactly soluble models of phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(2), pages 853-866.
    2. Brankov, J.G., 1990. "Finite-size effects in the approximating Hamiltonian method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(3), pages 1035-1054.
    3. 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.
    4. Chamati, Hassan, 1994. "T = 0 finite-size scaling for a quantum system with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(3), pages 357-368.
    5. Pisanova, E.S. & Tonchev, N.S., 1995. "Universal amplitudes in finite-size scaling for an anharmonic crystal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(3), pages 419-428.
    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.

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