21 research outputs found
Duals of U(N) LGT with staggered fermions
Various approaches to construction of dual formulations of non-abelian
lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of
the Weingarten functions to construct a dual formulation. In particular, the
dual representations are constructed 1) for pure gauge models in all
dimensions, 2) in the strong coupling limit for the models with arbitrary
number of flavours and 3) for two-dimensional U(N) QCD with staggered fermions.
Applications related to the finite temperature/density QCD are discussed.Comment: 8 pages, Proceedings for the 35th International Symposium on Lattice
Field Theory (Lattice 2017
Three-quark potentials in an effective Polyakov loop model
Three-quark potentials are studied in great details in the three-dimensional
pure gauge theory at finite temperature, for the cases of static
sources in the fundamental and adjoint representations. For this purpose, the
corresponding Polyakov loop model in its simplest version is adopted. The
potentials in question, as well as the conventional quark--anti-quark
potentials, are calculated numerically both in the confinement and
deconfinement phases. Results are compared to available analytical predictions
at strong coupling and in the limit of large number of colors . The
three-quark potential is tested against the expected and laws and
the string tension entering these laws is compared to the conventional
string tension. As a byproduct of this investigation, essential
features of the critical behaviour across the deconfinement transition are
elucidated.Comment: 28 pages, 18 figures, 4 tables; some text and a few references added;
version accepted for publication on Nucl. Phys.
Critical behavior of the compact 3d U(1) gauge theory on isotropic lattices
We report on the computation of the critical point of the deconfinement phase
transition, critical indices and the string tension in the compact three
dimensional U(1) lattice gauge theory at finite temperatures. The critical
indices govern the behavior across the deconfinement phase transition in the
pure gauge U(1) model and are generally expected to coincide with the critical
indices of the two-dimensional XY model. We studied numerically the U(1) model
for N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our
determination of the infinite volume critical point on the lattice with N_t=8
differs substantially from the pseudo-critical coupling at L=32, found earlier
in the literature and implicitly assumed as the onset value of the deconfined
phase. The critical index computed from the scaling of the
pseudo-critical couplings with the extension of the spatial lattice agrees well
with the XY value =1/2. On the other hand, the index shows large
deviation from the expected universal value. The possible reasons of such
behavior are discussed in details.Comment: 15 pages, 7 figures; version accepted for publication on J. Stat.
Mech
Critical behavior of 3D Z(N) lattice gauge theories at zero temperature
Three-dimensional lattice gauge theories at zero temperature are
studied for various values of . Using a modified phenomenological
renormalization group, we explore the critical behavior of the generalized
model for . Numerical computations are used to simulate
vector models for for lattices with linear extension up
to . We locate the critical points of phase transitions and establish
their scaling with . The values of the critical indices indicate that the
models with belong to the universality class of the three-dimensional
model. However, the exponent derived from the heat capacity is
consistent with the Ising universality class. We discuss a possible resolution
of this puzzle. We also demonstrate the existence of a rotationally symmetric
region within the ordered phase for all at least in the finite
volume.Comment: 25 pages, 4 figures, 8 table