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Journal of Mathematical Physics

A fully crossing symmetric vertex function

Michael Gering, W. D. Heiss

Published Feb 1, 1984• 2 citations
Publisher

Abstract

A fully crossing symmetric vertex function was calculated in an exactly soluble model. It has branch points in the interaction strength whose positions are independent of the energy variables. The irreducible vertex parts entering the Bethe–Salpeter equations are more involved than the vertex function itself.
DOI
10.1063/1.526154

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The Bethe-Ansatz approach is used to solve a nineteen-vertex model equivalent to a spin model with O(n) symmetry on the square lattice. The bulk free energy is determined exactly on four branches of critical points. On two of these branches, the central charge is derived from finite-size corrections. On the two other branches, the nature of the Bethe Ansatz solutions prevents us from computing the central charge analytically. In this case, our approach still allows the exact numerical determination of the free energy on strips of hundreds of sites wide.