Vortices and Magnetization in Kac’s Model

We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential $J_\gamma(i)=\gamma^2J(\gamma i)$, $J$ with compact support. The system is subject to boundary conditions with vorticity. Using a Glauber like dynamics, we compute minimizers of the free ener...

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Bibliographic Details
Published inJournal of statistical physics Vol. 128; no. 3; pp. 741 - 770
Main Authors Bouanani, H. El, Rouleux, M.
Format Journal Article
LanguageEnglish
Published Springer Verlag 01.08.2007
Subjects
Condensed Matter
Mathematical Physics
Mathematics
Physics
Statistical Mechanics
Belavin-Polyakov model
vortex
Gradient-flow dynamics
Kac's model
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ISSN0022-4715
1572-9613
DOI10.1007/s10955-007-9319-8

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Summary:We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential $J_\gamma(i)=\gamma^2J(\gamma i)$, $J$ with compact support. The system is subject to boundary conditions with vorticity. Using a Glauber like dynamics, we compute minimizers of the free energy functional at low temperature, i.e. in the regime of phase transition. We have the numerical evidence of a vortex structure for minimizers, which present many common features with those of the Ginzburg-Landau functional.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-007-9319-8