Spin lattice systems at low temperature

Author(s)

Kelvyn Emmanoel de Castro Martins Welsch de Souza

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2024-02-06

Examining board members

Rodrigo Bissacot Proença; Pierre Picco; Aldo Procacci

• Advisor: Rodrigo Bissacot Proença

Abstract

In this work, two main aspects of low-temperature spin systems are considered --- the cluster expansion for long-range Ising-type models and the construction of the phase diagram when quantum perturbations are present. With respect to the first subject, we present a new result stating that the cluster expansion does converge for interactions with polynomial decay \\alpha, for any \\alpha > d \\geq 2, provided that the contours are defined in a suitable manner. As for the second subject, we review a paper due to Borgs, Kotecký and Ueltschi, which extends Pirogov-Sinai theory and whose main result is that, even with quantum perturbations, the low-temperature phase diagram is homeomorphic to the zero-temperature one. (AU)

• FAPESP's process: 22/00746-1 - Spin and fermionic lattice systems in low temperature
• Grantee: Kelvyn Emmanoel de Castro Martins Welsch de Souza
• Support Opportunities: Scholarships in Brazil - Master