2004/10/31 by L. Li, Yannick Meurice, Y. Meurice
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Gauge theory #Ising model #Lattice gauge theory #Mathematical physics #Mathematics #Observable #Particle physics theoretical and experimental studies #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.71.016008
published as Phys.Rev. D71 (2005) 016008 · 7 pages, 7 figures, uses revtex, Eqs. 15-17 corrected, minor changes
arxiv created 2004/11/03 · openalex publication_date 2005/01/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider Wilson's SU(N) lattice gauge theory (without fermions) at negative values of \ensuremathβ=2N/g2 and for N=2 or 3. We show that in the limit \ensuremathβ\ensuremath→\ensuremath-\ensuremath∞, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected nonintersecting lines. For N=2, these configurations can be characterized by a unique gauge invariant set of variables, while for N=3 a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when g2 changes its sign which prevents us from having a convergent series in g2 for this quantity. For N=2, a change of variables relates the gauge invariant observables at positive and negative values of \ensuremathβ. For N=3, we derive an identity relating the observables at \ensuremathβ with those at \ensuremathβ rotated by \ifmmode±\else\textpm\fi2\ensuremathπ/3 in the complex plane and show numerical evidence for a Ising like first order phase transition near \ensuremathβ=\ensuremath-22. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.