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Bethe ansatz calculations for the eight-vertex model on a finite strip

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Abstract

Bethe ansatz equations for the eigenvalues of the transfer matrix of the eight-vertex model are solved numerically to yield mass gap data on infinitely long strips of up to 512 sites in width. The finite-size corrections, at criticality, to the free energy per site and polarization gap are found to be in agreement with recent studies of theXXZ spin chain. The leading corrections to the finite-size scaling estimates of the critical line and thermal exponent are also found, providing an explanation of the poor convergence seen in earlier studies. Away from criticality, the linear scaling fields are derived exactly in the full parameter space of the spin system, allowing a thorough test of a recently proposed method of extracting linear scaling fields and related exponents from finite lattice data.

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Author notes

  1. Michael N. Barber

    Present address: Department of Mathematics, The Faculties, Australian National University, 2601, Canberra, ACT, Australia

  2. Murray T. Batchelor

    Present address: Instituut-Lorentz voor Theoretische Natuurkunde, 2311, SB Leiden, The Netherlands

Authors and Affiliations

  1. Department of Mathematics, The Faculties, Australian National University, 2601, Canberra, ACT, Australia

    Murray T. Batchelor

  2. Institute for Theoretical Physics, University of California, 93106, Santa Barbara, California

    Michael N. Barber

  3. Department of Mathematics, University of Melbourne, 3052, Parkville, VIC, Australia

    Paul A. Pearce

Authors
  1. Murray T. Batchelor
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  2. Michael N. Barber
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  3. Paul A. Pearce
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Batchelor, M.T., Barber, M.N. & Pearce, P.A. Bethe ansatz calculations for the eight-vertex model on a finite strip. J Stat Phys 49, 1117–1163 (1987). https://doi.org/10.1007/BF01017563

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  • DOI: https://doi.org/10.1007/BF01017563

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