22 research outputs found
Center clusters in the Yang-Mills vacuum
Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory
at finite temperature are analyzed. We show that spatial clusters can be
identified where the local Polyakov loops have values close to the same center
element. For a suitable definition of these clusters the deconfinement
transition can be characterized by the onset of percolation in one of the
center sectors. The analysis is repeated for different resolution scales of the
lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE
Ward Identities for Invariant Group Integrals
We derive two types of Ward identities for the generating functions for
invariant integrals of monomials of the fundamental characters for arbitrary
simple compact Lie groups. The results are applied to the groups SU(3), Spin(5)
and G_2 of rank 2 as well as SU(4).Comment: 31 pages, 3 figures, LaTeX corrected typo
Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory
We present a study of the free energy of parameterized Polyakov loops P in
SU(2) and SU(3) lattice gauge theory as a function of the parameters that
characterize P. We explore temperatures below and above the deconfinement
transition, and for our highest temperatures T > 5 T_c we compare the free
energy to perturbative results.Comment: Minor changes. Final version to appear in JHE
Generalized Potts-Models and their Relevance for Gauge Theories
We study the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents ν and γ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model
Two-color QCD via dimensional reduction
We study the thermodynamics of two-color QCD at high temperature and/or
density using a dimensionally reduced superrenormalizable effective theory,
formulated in terms of a coarse grained Wilson line. In the absence of quarks,
the theory is required to respect the Z(2) center symmetry, while the effects
of quarks of arbitrary masses and chemical potentials are introduced via soft
Z(2) breaking operators. Perturbative matching of the effective theory
parameters to the full theory is carried out explicitly, and it is argued how
the new theory can be used to explore the phase diagram of two-color QCD.Comment: 17 pages, 1 eps figure, jheppub style; v2: minor update, references
added, published versio
Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series
We derive three-dimensional, Z(N)-symmetric effective actions in terms of
Polyakov loops by means of strong coupling expansions, starting from thermal
SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in
the literature, corresponding to the (spatial) strong coupling limit, is thus
extended by several higher orders, as well as by additional interaction terms.
We provide analytic mappings between the couplings of the effective theory and
the parameters of the original thermal lattice theory, which can
be systematically improved. We then investigate the deconfinement transition
for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the
effective theory. Our effective models correctly reproduce second order 3d
Ising and first order phase transitions, respectively. Furthermore, we
calculate the critical couplings and find agreement with
results from simulations of the 4d theory at the few percent level for
.Comment: 27 pages, 21 figures; final version published in JHEP; attached the
corresponding Erratum (ref. JHEP 1107:014,2011, DOI 10.1007/JHEP07(2011)014)
for ease of consultatio
Supersymmetric Nonlinear O(3) Sigma Model on the Lattice
A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime
dimensions is investigated by means of Monte Carlo simulations. We argue that
it is impossible to construct a lattice action that implements both the O(3)
symmetry as well as at least one supersymmetry exactly at finite lattice
spacing. It is shown by explicit calculations that previously proposed
discretizations fail to reproduce the exact symmetries of the target manifold
in the continuum limit. We provide an alternative lattice action with exact
O(3) symmetry and compare two approaches based on different derivative
operators. Using the nonlocal SLAC derivative for the quenched model on
moderately sized lattices we extract the value {\sigma}(2, u_0) = 1.2604(13)
for the step scaling function at u_0 = 1.0595, to be compared with the exact
value 1.261210. For the supersymmetric model with SLAC derivative the discrete
chiral symmetry is maintained but we encounter strong sign fluctuations,
rendering large lattice simulations ineffective. By applying the Wilson
prescription, supersymmetry and chiral symmetry are broken explicitly at finite
lattice spacing, though there is clear evidence that both are restored in the
continuum limit by fine tuning of a single mass parameter.Comment: 35 pages, 36 figures, 2 tables; updated version as accepted by JHE