3,247 research outputs found
Large N Phase Transitions and Multi-Critical Behaviour in Generalized 2D QCD
Using matrix model techniques we investigate the large N limit of generalized
2D Yang-Mills theory. The model has a very rich phase structure. It exhibits
multi-critical behavior and reveals a third order phase transitions at all
genera besides {\it torus}. This is to be contrasted with ordinary 2D
Yang-Mills which, at large N, exhibits phase transition only for spherical
topology.Comment: CERN-TH.7390/94 and TAUP-2191-94, 6pp, LaTe
A new large N phase transition in YM2
Inspired by the interpretation of two dimensional Yang-Mills theory on a
cylinder as a random walk on the gauge group, we point out the existence of a
large N transition which is the gauge theory analogue of the cutoff transition
in random walks. The transition occurs in the strong coupling region, with the
't Hooft coupling scaling as alpha*log(N), at a critical value of alpha (alpha
= 4 on the sphere). The two phases below and above the transition are studied
in detail. The effective number of degrees of freedom and the free energy are
found to be proportional to N^(2-alpha/2) below the transition and to vanish
altogether above it. The expectation value of a Wilson loop is calculated to
the leading order and found to coincide in both phases with the strong coupling
value.Comment: 23 pages, 3 figure
The Kazakov-Migdal Model as a High Temperature Lattice Gauge Theory
We show that the Kazakov-Migdal (K-M) induced gauge model in dimensions
describes the high temperature limit of ordinary lattice gauge theories in
dimensions. The matter fields are related to the Polyakov loops, while
the spatial gauge variables become the gauge fields of the K-M model. This
interpretation of the K-M model is in agreement with some recent results in
high temperature lattice QCD.Comment: 12 pages, plain latex, DFTT 71/9
Field Strength Correlators For 2D Yang-Mills Over Riemann Surfaces
The path integral computation of field strength correlation functions for two
dimensional Yang-Mills theories over Riemann surfaces is studied. The
calculation is carried out by abelianization, which leads to correlators that
are topological. They are nontrivial as a result of the topological
obstructions to the abelianization. It is shown in the large N limit on the
sphere that the correlators undergo second order phase transitions at the
critical point. Our results are applied to a computation of contractible Wilson
loops.Comment: final version to appear in Int. Jour. Mod. Phys. A, minor
corrections, added a few comments on Wilson loops and non-abelian Stokes
theore
Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory
Bayes statistics and statistical physics have the common mathematical
structure, where the log likelihood function corresponds to the random
Hamiltonian. Recently, it was discovered that the asymptotic learning curves in
Bayes estimation are subject to a universal law, even if the log likelihood
function can not be approximated by any quadratic form. However, it is left
unknown what mathematical property ensures such a universal law. In this paper,
we define a renormalizable condition of the statistical estimation problem, and
show that, under such a condition, the asymptotic learning curves are ensured
to be subject to the universal law, even if the true distribution is
unrealizable and singular for a statistical model. Also we study a
nonrenormalizable case, in which the learning curves have the different
asymptotic behaviors from the universal law
Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory
The free energy in the weak-coupling phase of two-dimensional Yang-Mills
theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using
the techniques of Gross and Matytsin. Many features of Yang-Mills theory are
universal among different gauge groups in the large N limit, but significant
differences arise in subleading order in 1/N.Comment: 10 pages; no figures; LaTe
Theta Sectors and Thermodynamics of a Classical Adjoint Gas
The effect of topology on the thermodynamics of a gas of adjoint
representation charges interacting via 1+1 dimensional SU(N) gauge fields is
investigated. We demonstrate explicitly the existence of multiple vacua
parameterized by the discrete superselection variable k=1,...,N. In the low
pressure limit, the k dependence of the adjoint gas equation of state is
calculated and shown to be non-trivial. Conversely, in the limit of high system
pressure, screening by the adjoint charges results in an equation of state
independent of k. Additionally, the relation of this model to adjoint QCD at
finite temperature in two dimensions and the limit of large N are discussed.Comment: 17 pages LaTeX, 3 eps figures, uses eps
- …