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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/2509.11797v3 (pdf) |
| Date submitted: | Jan. 26, 2026, 2:32 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
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At the end of page 6, we rewrote a sentence to avoid any ambiguity about the case in question (matrices B and C are non-invertible in the entire article).
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We have added a remark at the end of subsection 1.3 (now remark 1.3). This note specifies that local twists can be defined (which already exist in some studied models, for example the pDWBC model) but that we do not use them in this case in order to be able to complete our calculations.
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We add " = 0" to correct the formula (1.6).
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We change the notation of the statistical weights, \omega_i instead of w_i, to avoid writing conflicts with the coefficients of the vector <w|.
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In Figure 4c, we have darkened the dark blue curve to clearly separate it from the blue curve.
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We have corrected the typographical error in formula (A.32) : it is p-l, instead of l-p.
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We have corrected the equation number in [FW12] cited in remark B.2 to match the numbering in the published version (equation (3.14) in [FW12]).
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We have corrected the typographical error in formulae (D.6) and (D.7) : it is N, instead of n.