A equação de Yang-Baxter para modelos de vértices com três estados

• Autor(a) principal: Pimenta, Rodrigo Alves
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5029
• topic: Yang-Baxter (Equação); Modelos integráveis; Ansatz de Bethe; Yang-Baxter equation; Lattice integrable models; Bethe Ansatz; CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::FISICA MATEMATICA

In this work we study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the respective Boltzmann weights and found that they possess a universal structure. This allows us to classify the integrable manifolds in four different families reproducing three known models besides uncovering a novel nineteen vertex model in a unified way. The introduction of the spectral parameter on the weights is made via the parameterization of the fundamental algebraic curve which is a conic. The diagonalization of the transfer matrix of the new vertex model and its thermodynamic limit properties are discussed. We point out a connection between the form of the main curve and the nature of the excitations of the corresponding spin-1 chains.