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arXiv:1604.01223 · Physical review. E

Partition function of the elliptic solid-on-solid model as a single determinant

W. Galléas

Published Jul 5, 2016• 12 citations
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Abstract

In this Rapid Communication we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.
DOI
10.1103/physreve.94.010102

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The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ‘reconstruction’ formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.