Vortices and Magnetization in Kac's Model
Hicham El-Bouanani, Michel Rouleux
Abstract
We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential Jγ(i)=γ2J(γi), 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.
Create a lesson
Related papers
2-Morita Theory of E2-Algebras and Module Categories
Rongge Xu, Holiverse Yang
Multiscale Loop Vertex Expansion for Cumulants, the ϕ42 Model
Vincent Rivasseau
Quasi-polynomiality and N-point functions of single connected leaky completed Hurwitz numbers
Chongyu Wang, Chenglang Yang
Coupled stochastic variational principles for multiscale surface gravity waves -- Part I: theoretical framework
Etienne Mémin, Arnaud Debussche
The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
Jiawei He, Xueyin Wang
Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu