Algebraic curves of integrable models: theory and applications

• Grant number: 10/19839-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2011
• End date: July 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Marcio Jose Martins
• Grantee: Rodrigo Alves Pimenta
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 09/01804-0 - Physical mathematics of integrable systems, AP.TEM

Abstract

The aim of this project is to unveil the algebraic invariants governing integrable classical vertex models of statistical mechanics whose number of states per edge bigger or equal to three. This problem is of central interest in the field of exactly solved models since it has direct connection with the unsolved issue of classification of solutions of the Yang-Baxter equation. We also intend to investigate possible relationship between the geometric form of the main algebraic curve/surface with the nature of the excitations of the corresponding chain. (AU)