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International Journal of Modern Physics B

EXACT SPECTRUM OF THE INTEGRABLE 3-STATE POTTS CHAIN

Giuseppe Albertini, Srinandan Dasmahapatra, Barry M. McCoy

Published Sep 30, 1993• 3 citations
Publisher

Abstract

From a system of Bethe-Ansatz equations, the spectrum of low-lying excitations is found for the 3-state Potts chain in its ferromagnetic and antiferromagnetic version. In both cases, only massless excitations appear and their dispersion relations are computed.
DOI
10.1142/s0217979293003346

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All eigenvalues of the transfer matrix of the integrable 3-state Potts model are computed as polynomials in the spectral variable for chains of length M ≤7. The zeroes of the eigenvalues are known to satisfy a Bethe's Ansatz equation and thus it is of particular interest that we find many solutions whose zeroes do not satisfy the traditional "string hypothesis". We also find many cases where the integers in the logarithmic form of the Bethe equations do not satisfy the monotonicity properties that they are usually assumed to possess. We present a classification of all eigenvalues in terms of sets of roots and show that, for all M, this classification yields a complete set.
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A Bethe–Ansatz study of a self-dual ZN spin model is undertaken for even spin system. One must solve a coupled system of Bethe–Ansatz equations (BAE) involving zeroes of two families of transfer matrices. A numerical study on finite size lattices is done for identification of elementary excitations over the ferromagnetic and antiferromagnetic ground states. The free energies for both ferromagnetic and antiferromagnetic ground states and dispersion relation for elementary excitations are found.