bibkey: enciso2007nearestneighbor authors: A. Enciso; F. Finkel; A. González-López; M. A. Rodríguez year: 2007 title: “A novel quasi-exactly solvable spin chain with nearest-neighbors interactions” doi: 10.1016/j.nuclphysb.2007.07.001 url: https://arxiv.org/abs/0704.3046v1 claim: “The first one is the requirement that ξ be the unique minimum of the potential U in the domain C. Although our numerical calculations suggest that this is indeed the case, we have not been able to provide a rigorous proof of this fact.” strata_touched:

• D5/S3/Quantum/SpinChains/NearestNeighborFreezingUniqueMinimum
• D5/S3/Quantum/SpinChains/NearestNeighborLastSiteDivergence license: citation-only triage: anchor

A novel quasi-exactly solvable spin chain with nearest-neighbors interactions

A. Enciso, F. Finkel, A. González-López and M. A. Rodríguez, arXiv:0704.3046v1 (2007); Nucl. Phys. B 790 (2008), doi: 10.1016/j.nuclphysb.2007.07.001.

The paper states in the paragraph after Eqs. (31)–(32), printed p. 13:

“The first one is the requirement that ξ be the unique minimum of the potential U in the domain C. Although our numerical calculations suggest that this is indeed the case, we have not been able to provide a rigorous proof of this fact.”

Verified locator

• URL: https://arxiv.org/abs/0704.3046v1, §3, printed p. 13, after Eqs. (31)–(32).
• DOI: https://doi.org/10.1016/j.nuclphysb.2007.07.001. The DOI identifies the journal article; its full text is unverified. The quoted claim and formal statement concern the arXiv v1 text.

Last-site question

The same arXiv v1 source asks in §2, printed pp. 9–10, around Eq. (19):

It is also of interest to determine whether the position of the last spin tends to infinity as N → ∞, since according to our interpretation of the chain’s geometry the number 2ξN/π is the radius of the circle on which the spins lie.

The source motivates divergence by the inverse-error-function approximation in Eq. (19), then cautions that Eq. (18) is accurate only up to terms of order 1/N. The question concerns the cyclic site equations (6) in the strictly increasing chamber. The source’s site ξN is the zero-based coordinate N − 1 in NearestNeighborLastSiteDivergence.