Surface Critical Phenomena and Scaling in the Eight-Vertex Model

Details Surface Critical Phenomena and Scaling in the Eight-Vertex Model Surface Critical Phenomena and Scaling in the Eight-Vertex Model

1995-10-27

arxiv.org/abs/cond-mat/9510152v1

Phys.Rev.Lett.76:14-17,1996; Erratum-ibid.76:2826,1996

Physics

Condensed Matter

12 pages, LaTeX with REVTEX macros needed. To appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.76.14

We give a physical interpretation of the entries of the reflection $K$-matrices of Baxter's eight-vertex model in terms of an Ising interaction at an open boundary. Although the model still defies an exact solution we nevertheless obtain the exact surface free energy from a crossing-unitarity relation. The singular part of the surface energy is described by the critical exponents $\alpha_s = 2 - \frac{\pi}{2\mu}$ and $\alpha_1 = 1 - \frac{\pi}{\mu}$, where $\mu$ controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point $\mu=\pi/2$ and confirm the scaling relations $\alpha_s = \alpha_b + \nu$ and $\alpha_1 = \alpha_b -1$.

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