Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.12.016· OSTI ID:21579908

Mehta, Dhagash ^[1]; Kastner, Michael ^[2]

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1. Department of Physics, Syracuse University, Syracuse, NY 13244 (United States)
2. National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa)

Research Highlights: > Exact results for all stationary points of some high-dimensional function are given. > They are interpreted as Gribov copies of a lattice Landau gauge fixing functional. > The Gribov ambiguity and the Neuberger problem in compact U(1) are illustrated. > Stationary points are used to discuss a criterion on the absence of phase transitions. - Abstract: 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.

• OSTI ID: 21579908
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 6; Other Information: DOI: 10.1016/j.aop.2010.12.016; PII: S0003-4916(11)00031-5; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
GAUGE INVARIANCE
HAMILTONIANS
ONE-DIMENSIONAL CALCULATIONS
PARTITION FUNCTIONS
PERIODICITY
PHASE TRANSFORMATIONS
RANDOMNESS
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
QUANTUM OPERATORS
VARIATIONS