Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-10-26
Annals Phys.326:1425-1440,2011
Physics
Condensed Matter
Statistical Mechanics
17 pages, 2 figures
Scientific paper
10.1016/j.aop.2010.12.016
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.
Kastner Michael
Mehta Dhagash
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