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Finite-size effects in the approximating Hamiltonian method

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  • Brankov, J.G.

Abstract

The Husimi-Temperley mean spherical model, in which each two particles interact with equal strength, is considered. This model is shown to be equivalent to a d-dimensional model with periodic boundary conditions and interaction potential σJσ(r), where Jσ(r) ∼ r−d−σ as r→∞, σ > 0 being a parameter, in the limit σ→0. It is found that the approximating Hamiltonian method yields singular finite-size scaling functions both in the neighbourhood of the critical point and near a first-order phase transition. A modification of this method is suggested, which allows for all the essential configurations and reproduces the exact finite-size scaling near a first-order phase transition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:168:y:1990:i:3:p:1035-1054
    DOI: 10.1016/0378-4371(90)90270-3
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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. Brankov, J.G. & Danchev, D.M., 1987. "Ground state of an infinite two-dimensional system of dipoles on a lattice with arbitrary rhombicity angle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(1), pages 128-139.
    4. Brankov, J.G. & Danchev, D.M., 1989. "A probabilistic view on finite-size scaling in infinitely coordinated spherical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 158(3), pages 842-863.
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