SEMINAR @ SISSSA, M. Cicalese 24 July at 16.00 hrs.

[Barbara Corzani]

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FUNCTIONAL ANALYSIS SECTOR'S ACTIVITIES
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SEMINAR 

Dott. 
Marco Cicalese
(Università di Napoli)


Title:
"A variational approach to the ground states of the XY model"
 
Tue. 24 July 2007  @  04.00 p.m.

SISSA - Main Building - ground floor - room B

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Abstract:
The discrete structure of the ground states of a spin system is often neglected
by introducing a mesoscopic scale that captures the main features of the
problem while simplifying its analysis. In general this procedure is not
rigorous and not even well understood. In this seminar we will show that in the
case of the ground states of the XY (N dimensional possibly anysotropic) spin
type models it is indeed possible to justify, from a variational point of view,
the coarse graining procedure which leads to a Ginzburg-Landau type energy on a
mesoscopic scale. Topological type phase transitions will be
highlighted by showing the presence of vortice-like ground states. In the
2-dimesional case we will show how it is possible to address the problem in the
case of long range interactions. Finally we will discuss several possible
developments and present some open problems.