180 research outputs found
The topological properties of QCD at high temperature: problems and perspectives
Lattice computations are the only first principle method capable of
quantitatively assessing the topological properties of QCD at high temperature,
however the numerical determination of the topological properties of QCD,
especially in the high temperature phase, is a notoriously difficult problem.
We will discuss the difficulties encountered in such a computation and some
strategies that have been proposed to avoid (or at least to alleviate) them.Comment: 12 pages, 5 eps figs. Talk given at the 35th International Symposium
on Lattice Field Theory, 18-24 June 2017, Granada (Spain
Topology and dependence in finite temperature lattice gauge theory
In this work we study the topological properties of the lattice gauge
theory by means of Monte Carlo simulations. We focus on the behaviour of
topological quantities across the deconfinement transition and investigate
observables related to the dependence of the free energy. As in
gauge theories, an abrupt change happens at deconfinement and an
instanton gas behaviour rapidly sets in for .Comment: 11 pages, 8 eps figures (typos corrected in eq.2.5 and 2.7 with
respect to the published version
The Peierls argument for higher dimensional Ising models
The Peierls argument is a mathematically rigorous and intuitive method to
show the presence of a non-vanishing spontaneous magnetization in some lattice
models. This argument is typically explained for the Ising model in a way
which cannot be easily generalized to higher dimension. The aim of this paper
is to present an elementary discussion of the Peierls argument for the general
-dimensional Ising model.Comment: 14 pages, 5 eps figures, minor change
Color flux tubes in Yang-Mills theory: an investigation with the connected correlator
In this work we perform an investigation of the flux tube between two static
color sources in four dimensional Yang-Mills theory, using the so
called connected correlator. Contrary to most previous studies we do not use
any smoothing algorithm to facilitate the evaluation of the correlator, that is
performed using only stochastically exact techniques. We first examine the
renormalization properties of the connected operator, then we present our
numerical data for the longitudinal chromoelectric component of the flux tube,
that are used to extract the dual superconductivity parameters.Comment: 8 pages, 6 eps 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.
The three-dimensional, three state Potts model in a negative external field
We investigate the critical behaviour of the three-dimensional, three state
Potts model in presence of a negative external field h, i.e. disfavouring one
of the three states. A genuine phase transition is present for all values of
|h|, corresponding to the spontaneous breaking of a residual Z_2 symmetry. The
transition is first/second order respectively for small/large values of |h|,
with a tricritical field h_tric separating the two regimes. We provide, using
different and consistent approaches, a precise determination of h_tric; we also
compare with previous studies and discuss the relevance of our investigation to
analogous studies of the QCD phase diagram in presence of an imaginary chemical
potential.Comment: 11 pages, 17 figures, minor correction
The topological susceptibility of two-dimensional gauge theories
In this paper we study the topological susceptibility of two-dimensional
gauge theories. We provide explicit expressions for the partition
function and the topological susceptibility at finite lattice spacing and
finite volume. We then examine the particularly simple case of the abelian
theory, the continuum limit, the infinite volume limit, and we finally
discuss the large limit of our results.Comment: 11 pages, 7 eps figure
Universal scaling effects of a temperature gradient at first-order transitions
We study the effects of smooth inhomogeneities at first-order transitions. We
show that a temperature gradient at a thermally-driven first-order transition
gives rise to nontrivial universal scaling behaviors with respect to the length
scale of the variation of the local temperature T(x). We propose a scaling
ansatz to describe the crossover region at the surface where T(x)=Tc, where the
typical discontinuities of a first-order transition are smoothed out.
The predictions of this scaling theory are checked, and get strongly
supported, by numerical results for the 2D Potts models, for a sufficiently
large number of q-states to have first-order transitions. Comparing with
analogous results at the 2D Ising transition, we note that the scaling
behaviors induced by a smooth inhomogeneity appear quite similar in first-order
and continuous transitions.Comment: 8 page
dependence in Yang-Mills theory from analytic continuation
We investigate the topological properties of the pure gauge theory by
performing numerical simulations at imaginary values of the parameter.
By monitoring the dependence of various cumulants of the topological charge
distribution on the imaginary part of and exploiting analytic
continuation, we determine the free energy density up to the sixth order order
in , . That permits us to achieve
determinations with improved accuracy, in particular for the higher order
terms, with control over the continuum and the infinite volume extrapolations.
We obtain and .Comment: 10 pages, 9 eps figures (minor changes
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