Advanced Studies in Pure Mathematics

A New Family of Solvable Lattice Models Associated with $A_{n}^{(1)}$

A. Kuniba

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Abstract

Presented is a new family of solvable solid-on-solid models in two-dimensional statistical mechanics. The site variables take the values in a set of not necessarily dominant integral weights of the affine Lie algebra $A^{(1)}_n$. The local state probabilities are obtained and the critical behavior is studied. Our family gives an extension of some recently discovered hierarchies of solvable solid-on-solid models.

Article information

Source
Integrable Systems in Quantum Field Theory and Statistical Mechanics, M. Jimbo, T. Miwa and A. Tsuchiya, eds. (Tokyo: Mathematical Society of Japan, 1989), 367-398

Dates
Received: 20 December 1988
First available in Project Euclid: 17 June 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1529259758

Digital Object Identifier
doi:10.2969/aspm/01910367

Mathematical Reviews number (MathSciNet)
MR1048601

Zentralblatt MATH identifier
0712.17022

Citation

Kuniba, A. A New Family of Solvable Lattice Models Associated with $A_{n}^{(1)}$. Integrable Systems in Quantum Field Theory and Statistical Mechanics, 367--398, Mathematical Society of Japan, Tokyo, Japan, 1989. doi:10.2969/aspm/01910367. https://projecteuclid.org/euclid.aspm/1529259758


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