Frozen States for Short-Range Interaction Models with Four Spin States

• Grant number: 25/05034-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eduardo Garibaldi
• Grantee: Murilo Felício Nascimento dos Santos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 24/04685-2 - Thermodynamical and geometrical approach to multi dimensional aperiodic structures, AP.R

Abstract

This project is dedicated to the study of the zero-temperature convergence of equilibrium states for one-dimensional spin models with a finite number of spin states, with particular emphasis on the case in which the spin variable can take on four distinct values. We consider models whose phase space is the integer lattice Z, where particle interactions occur only between nearest neighbors. Such convergence will be investigated through algebraic and probabilistic properties naturally associated with the corresponding transfer matrices, their maximal positive eigenvalues (ensured by the Perron-Frobenius Theorem), and their respective positive-entry unit eigenvectors. (AU)