Integrable Boundaries in Statistical Mechanics

• Grant number: 12/13126-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: October 01, 2012
• End date: May 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Antonio Lima Santos
• Grantee: Rodrigo Alves Pimenta
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The aim of this project is to study the reflection equationfor R-matrices, solutions of the Yang-Baxter equation,that violate the symmetries usually assumed in this context.In particular, we shall analyze the reflection equation for three-statevertex models violating the charge symmetry,for models with R-matrix enjoying additiveand non-additive spectral parameters andfor nineteen-vertex models whose Boltzmann weights are parameterizedby curves of genus greater than or equal to one.For all these models, we shall try to answer the question: what is the variety dictated by the reflection equation?

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PIMENTA, R. A.; LIMA-SANTOS, A.. Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, NOV 2014. (11/18729-1, 12/13126-0)

PIMENTA, R. A.; LIMA-SANTOS, A.. Algebraic Bethe ansatz for the six vertex model with upper triangular K-matrices. Journal of Physics A-Mathematical and Theoretical, v. 46, n. 45, NOV 15 2013. (11/18729-1, 12/13126-0)

PIMENTA, R. A.; LIMA-SANTOS, A.. Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, v. N/A, p. 26-pg., 2014-11-01. (11/18729-1, 12/13126-0)