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Finite-size scaling and the isotropic spin-one antiferromagnetic chain

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  • Blöte, H.W.J.
  • Capel, H.W.

Abstract

We have applied finite-size scaling in the neighbourhood of the exactly solved point of the spin-one isotropic, antiferromagnetic chain with bilinear and biquadratic exchange interactions with opposite sign. Finite-size data for the ground-state energies and the gaps were obtained numerically for systems up to a length of 12 spins. Our results indicate that the criticality at the exactly solved point is unstable with respect to two perturbations, i.e. anisotropy, and a change of the ratio between bilinear and biquadratic interactions. This agrees qualitatively with recent results of Affleck; however, our results for the exponents associated with these operators do not agree satisfactorily. Finally, we present the critical line in the plane of these two perturbations.

Suggested Citation

  • Blöte, H.W.J. & Capel, H.W., 1986. "Finite-size scaling and the isotropic spin-one antiferromagnetic chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 139(2), pages 387-394.
    • Handle: RePEc:eee:phsmap:v:139:y:1986:i:2:p:387-394
    DOI: 10.1016/0378-4371(86)90127-5
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    References listed on IDEAS

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    1. Blöte, H.W.J & Nightingale, M.P, 1982. "Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 405-465.
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