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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| Published in | Journal of statistical physics Vol. 128; no. 3; pp. 741 - 770 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Springer Verlag
01.08.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-4715 1572-9613 |
| DOI | 10.1007/s10955-007-9319-8 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Bouanani, H. El Rouleux, M. |
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| Cites_doi | 10.1103/PhysRevE.57.6377 10.1017/S0956792501004752 10.1007/BF02179792 10.1007/BF02186812 10.1126/science.220.4598.671 10.1090/crmp/012/16 10.1007/978-1-4612-0287-5 10.1142/4090 10.1007/978-3-0348-8053-4_2 10.1023/A:1023095619236 10.1007/BF01028674 |
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| Keywords | Belavin-Polyakov model vortex Gradient-flow dynamics Kac's model |
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| Snippet | 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... |
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| Title | Vortices and Magnetization in Kac’s Model |
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