2010/10/26 by Dhagash Mehta, Michael Kastner
Physics and Astronomy · #AKA #Classical XY model #Gauge theory #Hamiltonian (control theory) #Hamiltonian lattice gauge theory #Lattice (music) #Lattice field theory #Lattice gauge theory #Quantum many-body systems #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1016/j.aop.2010.12.016
published as Annals Phys.326:1425-1440,2011 · 17 pages, 2 figures
arxiv created 2010/10/26 · openalex publication_date 2011/02/11 · arxiv updated 2011/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.