Statistical mechanics of vortices from field theory

Statistical Mechanics of Vortices from Field Theory

We study with lattice Monte Carlo simulations the interactions and macroscopic behaviour of a large number of vortices in the 3-dimensional U(1) gauge+Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength H c , the thermodynamical discontinuities, an...

Conformal Field Theory and Statistical Mechanics∗

Statistical Mechanics of Vortices from D-branes and T-duality

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian ...

Towards a Statistical Mechanics of Nonabelian Vortices

A detailed study is presented of classical field configurations describing nonabelian vortices in two spatial dimensions, when a global SO(3) symmetry is spontaneously broken to a discrete group IK isomorphic to the group of integers mod 4. The vortices in this model are characterized by the nonabelian fundamental group π1(SO(3)/IK) =Q8, which is isomorphic to the group of quaternions. We prese...

The Connection Between Statistical Mechanics and Quantum Field Theory

A four part series of lectures on the connection of statistical mechanics and quantum field theory. The general principles relating statistical mechanics and the path integral formulation of quantum field theory are presented in the first lecture. These principles are then illustrated in lecture 2 by a presentation of the theory of the Ising model for H = 0, where both the homogeneous and rando...