Topological Transitions in Spin Glass Systems

Boyal, Prasun (2017) Topological Transitions in Spin Glass Systems. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Prasun Boyal (12MS094)) 12MS094.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Spin glass systems has been studied. The difference between a disordered state and a traditional ordered state is discussed. The proper order parameter for a spin glass system is defined. The necessary condition for a system to show a glassy behaviour is investigated. Then a simple model having those conditions, namely the Sherrington-Kirkpatrick model is studied in details. Parisi's exact solution through replica symmetry method has been studied. Next topological aspect of a disordered system is looked upon. Defining various topological invariant operator, we studied particular topological invariances that a Hamiltonian possess. Using these topological invariances, we argue the presence of steps in transverse magnetization. These arguments are supported with exact diagonalisation results.

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