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Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits
by Matthieu Cornillault, Samuel Belliard
Submission summary
| Authors (as registered SciPost users): | Matthieu Cornillault |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2509.11797v2 (pdf) |
| Date submitted: | Oct. 16, 2025, 2:46 p.m. |
| Submitted by: | Matthieu Cornillault |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
We used an generative AI (ChatGPT in November 2024) to write a function in Wolfram Mathematica that computes the complete symmetric polynomials. This function helped us to verify our theoretical computations for the inverse matrix of the partial Cauchy matrix (proposition A.2).
Abstract
We continue the work of Belliard, Pimenta and Slavnov (2024) studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified Izergin one and a Vandermonde one. This expression enables us to compute the partition function in the homogeneous limit for the rectangular lattice, and then to study the thermodynamic limit. It leads to a new result, we obtain the first order of free energy with boundary effects in the thermodynamic limit.
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