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On the finite-size scaling in quantum critical phenomena

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  • Tonchev, N.S.

Abstract

An exactly solvable d-dimentional model of a structural phase transition, confined to a geometry Ld−d× ∞d are subjected to periodic boundary conditions, is considered in the low-temperature region. It is shown that in this region quantum effects are essential and that borderline dimensionalities between which finite-size scaling holds do not coincide with the lower and upper critical dimensionalities for the bulk system. A generalized version of the dimensional cross-over rule is established, i.e., the finite-size scaling behaviour of a d-dimensional system finite in d∗ = d−d' directions in the quantum limit is equivalent to the finite-size scaling behaviour of the classical (d + 1)-dimensional system, also finite in d∗ directions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:171:y:1991:i:2:p:374-383
    DOI: 10.1016/0378-4371(91)90284-J
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Haemers, W.H. & Parker, C. & Pless, V. & Tonchev, V.D., 1990. "A design and a code invariant under the simple group Co3," Research Memorandum FEW 458, Tilburg University, School of Economics and Management.
    4. 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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    Cited by:

    1. 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.

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