## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- 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

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

#### 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

**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