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Universal amplitudes in finite-size scaling for an anharmonic crystal

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  • Pisanova, E.S.
  • Tonchev, N.S.

Abstract

We consider an exactly solvable d-dimensional lattice model of an anharmonic crystal confined to a geometry Ld−d × ∞d′ and subject to periodic boundary conditions. The general idea of finite-size scaling on the whole phase diagram is tested and the universal amplitudes of the correlation length near the upper and lower critical dimensions in both the classifical and the quantum multicritical points are computed. A detailed analysis is given in terms of the dimensions d and d′ of the lattice and parameter σ of the harmonic force decreasing at long distances as 1/rd + σ (0 ⩽ σ ⩽ 2).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:217:y:1995:i:3:p:419-428
    DOI: 10.1016/0378-4371(95)00054-B
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    References listed on IDEAS

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    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. 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.
    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.
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    1. Pisanova, E.S. & Tonchev, N.S., 1996. "Modified finite-size scaling for anharmonic crystals with quantum fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(3), pages 325-333.

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