## Abstract

The fusion model of the L-state cyclic solid-on-solid (CSOS) model is considered at criticality. Each Z_{L}-charge sector of the fusion CSOS model is related to a sum of total spin sectors of the fusion vertex model with a seam on which the vertex weights are modified by a phase factor. The latter in turn becomes the higher-spin XXZ quantum chain with a twisted boundary condition in the extremely anisotropic limit. Using the known operator content of the higher-spin XXZ chain, the authors deduce that of the fusion CSOS model. The modular invariant partition function of the fusion CSOS at fusion level k is a sum of products of the Z(k) parafermionic and free boson sectors with the effective coupling g'=L^{2}(k-lambda/pi) for L odd and g"=L ^{2}(1/k-lambda/pi)/4 for L even, where lambda is the crossing parameter. Where L is odd and a multiple of k, or when L/2 is a multiple of k for L even, the modular invariant partition function becomes a simple product of the Z(k) parafermionic and the Gaussian partition function.

Original language | English |
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Article number | 010 |

Pages (from-to) | 51-62 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - 1993 |