Maximum temperature for an Ideal Gas of U^(1)\hat U(1) Kac-Moody Fermions

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the $\hat U(1)$ case is shown to have a maximum temperature $kT_{M} = |\lambda| /\pi$, where $\lambda$ is the coupling of the super charge operator $G_0$ to the fermions. This result is similar to the case of strings but unlike strings the result is obtained from a well-defined lagrangian.Comment: Needs subeqnarray.sty; To be published in Phys. Rev. D, Dec 15, 1995. Some typographical errors have been corrected in the revised versio

Vortices in small superconducting disks

We study the Ginzburg-Landau equations in order to describe a two-dimensional superconductor in a bounded domain. Using the properties of a particular integrability point ($\kappa = 1/ \sqrt2$) of these nonlinear equations which allows vortex solutions, we obtain a closed expression for the energy of the superconductor. The presence of the boundary provides a selection mechanism for the number of vortices. A perturbation analysis around $\kappa = 1/ \sqrt2$ enables us to include the effects of the vortex interactions and to describe quantitatively the magnetization curves recently measured on small superconducting disks. We also calculate the optimal vortex configuration and obtain an expression for the confining potential away from the London limit.Comment: 4 pages, to be published in Physica C (Superconductivity