An integrable nineteen vertex model lying on a hypersurface

Autor(es)

Martins, M. J. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Fis, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Nuclear Physics B; v. 892, p. 306-336, MAR 2015.
• Citações Web of Science: 3

Resumo

We have found a family of solvable nineteen vertex model with statistical configurations invariant by the time reversal symmetry within a systematic study of the respective Yang-Baxter relation. The Boltzmann weights sit on a degree seven algebraic threefold which is shown birationally equivalent to the three-dimensional projective space. This permits to write parameterized expressions for both the transition operator and the R-matrix depending on three independent affine spectral parameters. The Hamiltonian limit tells us that the azimuthal magnetic field term is connected with the asymmetry among two types of spectral variables. The absence of magnetic field defines a physical submanifold whose geometrical properties are remarkably shown to be governed by a quartic K3 surface. This expands considerably the class of irrational manifolds that could emerge in the theory of quantum integrable models. (C) 2015 The Author. Published by Elsevier B.V. (AU)

• Processo FAPESP: 13/21466-8 - Sistemas integráveis e geometria algébrica
• Beneficiário: Marcio Jose Martins
• Modalidade de apoio: Auxílio à Pesquisa - Regular