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The critical exponent η of the planar model from one-dimensional quantum field theory

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  • den Nijs, Marcel

Abstract

The one-dimensional quantum field approach of Luther and Scalapino to describe the critical properties of the planar model is reviewed. The model they use is a one-dimensional spin-1 model with impurities. It is shown that the continuum limit version of this model, which is obtained by replacing the lattice by a cut-off in momentum space, does not describe the original spin-1 model, but instead a region of the phase diagram where the impurity excitations are massless. Still the results are consistent with those of Kosterlitz and Thouless if backward scattering and umklapp processes are taken into account in the derivation of the continuum limit. The critical exponent of η is equal to 14 at the infinite-order phase transition.

Suggested Citation

  • den Nijs, Marcel, 1982. "The critical exponent η of the planar model from one-dimensional quantum field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 111(1), pages 273-287.
    • Handle: RePEc:eee:phsmap:v:111:y:1982:i:1:p:273-287
    DOI: 10.1016/0378-4371(82)90093-0
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    Cited by:

    1. Glaus, U., 1987. "The spin-1 Heisenberg chain with uniaxial anisotropy and its classical counterpart," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(2), pages 295-317.
    2. Thouless, D.J. & Tan, Yong, 1991. "Scaling, localization and bandwidths for equations with competing periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 177(1), pages 567-577.

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