264 research outputs found
Study of dependence in Yang-Mills theories on the lattice
We discuss the use of field theoretical techniques in the lattice
determination of the free energy dependence on the angle in SU(N)
Yang-Mills theories.Comment: 5 pages. Talk at the International Workshop on QCD: QCD@Work 2003 -
Conversano (Italy) 14-18 June 2003 (eConf C030614
Lattice QCD with purely imaginary sources at zero and non-zero temperature
We discuss various aspects and recent progress concerning lattice QCD studies
in the presence of external sources. We focus, in particular, on issues
regarding QCD with non-zero imaginary chemical potentials or with a
-term, and on the properties of strongly interacting matter in the
presence of electromagnetic background fields.Comment: 15 pages, 2 figures, plenary talk at the 32nd International Symposium
on Lattice Field Theory (23-28 June 2014, Columbia University, New York, NY,
USA). Minor changes, references adde
Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice
We discuss the extension of the field theoretical approach, already used in
the lattice determination of the topological susceptibility, to the computation
of further terms in the expansion of the ground state energy around
in SU(N) Yang-Mills theories. In particular we determine the
fourth order term in the expansion for SU(3) pure gauge theory and compare our
results with previous cooling determinations. In the last part of the paper we
make some considerations about the nature of the ultraviolet fluctuations
responsible for the renormalization of the lattice topological charge
correlation functions; in particular we propose and test an ansatz which leads
to improved estimates of the fourth and higher order terms in the expansion of
F(\theta).Comment: 20 page
High-Temperature QCD: theory overview
We review the recent progress achieved in the theoretical investigation of
Quantum Chromodynamics in the high temperature regime, with a focus on results
achieved by lattice QCD simulations. The discussion covers the structure of the
phase diagram and the properties of the strongly interacting medium at finite T
and small baryon chemical potential.Comment: 7 pages, 2 figures, Proceedings of the Quark Matter 2018 conference,
Venice, Ital
Imaginary chemical potentials and the phase of the fermionic determinant
A numerical technique is proposed for an efficient numerical determination of
the average phase factor of the fermionic determinant continued to imaginary
values of the chemical potential. The method is tested in QCD with eight
flavors of dynamical staggered fermions. A direct check of the validity of
analytic continuation is made on small lattices and a study of the scaling with
the lattice volume is performed.Comment: 6 pages, 6 figure
Topological critical slowing down: variations on a toy model
Numerical simulations of lattice quantum field theories whose continuum
counterparts possess classical solutions with non-trivial topology face a
severe critical slowing down as the continuum limit is approached. Standard
Monte-Carlo algorithms develop a loss of ergodicity, with the system remaining
frozen in configurations with fixed topology. We analyze the problem in a
simple toy model, consisting of the path integral formulation of a quantum
mechanical particle constrained to move on a circumference. More specifically,
we implement for this toy model various techniques which have been proposed to
solve or alleviate the problem for more complex systems, like non-abelian gauge
theories, and compare them both in the regime of low temperature and in that of
very high temperature. Among the various techniques, we consider also a new
algorithm which completely solves the freezing problem, but unfortunately is
specifically tailored for this particular model and not easily exportable to
more complex systems.Comment: 18 pages, 14 eps figures. Some changes and references added. To be
published by Phys Rev
Phase diagram of the 4D U(1) model at finite temperature
We explore the phase diagram of the 4D compact U(1) gauge theory at finite
temperature as a function of the gauge coupling and of the compactified
Euclidean time dimension L_t. We show that the strong-to-weak coupling
transition, which is first order at T=0 (L_t=\infty), becomes second order for
high temperatures, i.e. for small values of L_t, with a tricritical temporal
size \bar{L_t} located between 5 and 6. The critical behavior around the
tricritical point explains and reconciles previous contradictory evidences
found in the literature.Comment: minor changes, version published on Phys. Rev.
Phase structure of compactified gauge theories in magnetic backgrounds
We discuss the properties of non-abelian gauge theories formulated on
manifolds with compactified dimensions and in the presence of fermionic fields
coupled to magnetic backgrounds. We show that different phases may emerge,
corresponding to different realizations of center symmetry and translational
invariance, depending on the compactification radius and on the magnitude of
the magnetic field. Our discussion focuses on the case of an gauge
theory in 4 dimensions with fermions fields in the fundamental representation,
for which we provide some exploratory numerical lattice results.Comment: 5 pages, 7 figure
Finite size phase transitions in QCD with adjoint fermions
We perform a lattice investigation of QCD with three colors and 2 flavors of
Dirac (staggered) fermions in the adjoint representation, defined on a 4d space
with one spatial dimension compactified, and study the phase structure of the
theory as a function of the size Lc of the compactified dimension. We show that
four different phases take place, corresponding to different realizations of
center symmetry: two center symmetric phases, for large or small values of Lc,
separated by two phases in which center symmetry is broken in two different
ways; the dependence of these results on the quark mass is discussed. We study
also chiral properties and how they are affected by the different realizations
of center symmetry; chiral symmetry, in particular, stays spontaneously broken
at the phase transitions and may be restored at much lower values of the
compactification radius. Our results could be relevant to a recently proposed
conjecture of volume indepedence of QCD with adjoint fermions in the large Nc
limit.Comment: 9 pages, 12 figures; extended discussion about the chiral limit and
the chiral properties; 2 figures and references adde
Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation
We propose a new method to characterize the different phases observed in the
non-perturbative numerical approach to quantum gravity known as Causal
Dynamical Triangulation. The method is based on the analysis of the eigenvalues
and the eigenvectors of the Laplace-Beltrami operator computed on the
triangulations: it generalizes previous works based on the analysis of
diffusive processes and proves capable of providing more detailed information
on the geometric properties of the triangulations. In particular, we apply the
method to the analysis of spatial slices, showing that the different phases can
be characterized by a new order parameter related to the presence or absence of
a gap in the spectrum of the Laplace-Beltrami operator, and deriving an
effective dimensionality of the slices at the different scales. We also propose
quantities derived from the spectrum that could be used to monitor the running
to the continuum limit around a suitable critical point in the phase diagram,
if any is found.Comment: 21 pages, 26 figures, 2 table
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