Discrete Holomorphic Parafermions in the Eight Vertex Model

2012/09/19 by M. Tanhayi-Ahari, S. Rouhani, Tanhayi-Ahari, M. +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1209.4253

openalex publication_date 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that holomorphic Parafermions exist in the eight vertex model. This is done by extending the definition from the six vertex model to the eight vertex model utilizing a parameter redefinition. These Parafermions exist on the critical plane and integrable cases of the eight vertex model. We show that for the case of staggered eight vertex model, these Parafermions correspond to those of the Ashkin-Teller model. Furthermore, the loop representation of the eight vertex model enabled us to show a connection with the O(n) model which is in agreement with the six vertex limit found as a special case of the O(n) model.

Citations

• Condensation of fractional excitons, non-Abelian states in double-layer quantum Hall systems and Z₄ parafermions
• Discrete Holomorphicity at Two-Dimensional Critical Points

Related

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