Spin lattice systems at low temperature
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 clust...
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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2024 |
| Country: | Brasil |
| Institution: | Universidade de São Paulo (USP) |
| Repository: | Biblioteca Digital de Teses e Dissertações da USP |
| Language: | English |
| OAI Identifier: | oai:teses.usp.br:tde-26022024-174722 |
| Online Access: | https://www.teses.usp.br/teses/disponiveis/45/45132/tde-26022024-174722/ |
| Access Level: | Open access |
| Keyword: | Cluster expansion Expansão em polímeros Hubbard Long-range Longo-alcance Mecânica estatística quântica Pirogov-Sinai Quantum statistical mechanics |
| Summary: | 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. |
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