Computational Science and Engineering (CSE) Seminars

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CSE Seminar - "Heisenberg and XY models of Ferromagnets and Superconductors"

Event Type
Computational Science and Engineering
2240 Digital Computer Laboratory
Mar 27, 2013   12:00 pm  
Prof. Kay Kirkpatrick, Mathematics

There are several statistical mechanical models of ferromagnetism beyond the Ising model: the more realistic and challenging classical Heisenberg model, where the spins are in the 2-sphere instead of in {-1,+1}; and the XY model, where the spins are in the circle, which is also used to model superconductors.

Recent work with Elizabeth Meckes sheds some light on the qualitative behavior of the 3D Heisenberg model, by studying the Heisenberg model on a complete graph with the number of vertices going to infinity. Our results include detailed descriptions of the total spin through a second-order phase transition. I will also discuss work in progress on metastability in the XY model and goals for a related model of zero-temperature metallic states.

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