1,644 research outputs found
A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
By applying the recently developed nonperturbative functional renormalization
group (FRG) approach, we study the interplay between ferromagnetism, quasi-long
range order (QLRO) and criticality in the -dimensional random field O(N)
model in the whole (, ) diagram. Even though the "dimensional reduction"
property breaks down below some critical line, the topology of the phase
diagram is found similar to that of the pure O(N) model, with however no
equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that
QLRO, namely a topologically ordered "Bragg glass" phase, is absent in the
3--dimensional random field XY model. The nonperturbative results are
supplemented by a perturbative FRG analysis to two loops around .Comment: 4 pages, 4 figure
Asymptotically free four-fermion interactions and electroweak symmetry breaking
We investigate the fermions of the standard model without a Higgs scalar.
Instead, we consider a non-local four-quark interaction in the tensor channel
which is characterized by a single dimensionless coupling . Quantization
leads to a consistent perturbative expansion for small . The running of
is asymptotically free and therefore induces a non-perturbative scale
, in analogy to the strong interactions. We argue that
spontaneous electroweak symmetry breaking is triggered at a scale where
grows large and find the top quark mass of the order of . We also
present a first estimate of the effective Yukawa coupling of a composite Higgs
scalar to the top quark, as well as the associated mass ratio between the top
quark and the W boson.Comment: 24 page
Quantum simulation of lattice gauge theories using Wilson fermions
Quantum simulators have the exciting prospect of giving access to real-time
dynamics of lattice gauge theories, in particular in regimes that are difficult
to compute on classical computers. Future progress towards scalable quantum
simulation of lattice gauge theories, however, hinges crucially on the
efficient use of experimental resources. As we argue in this work, due to the
fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian,
the lattice representation of gauge theories allows for an optimization that up
to now has been left unexplored. We exemplify our discussion with lattice
quantum electrodynamics in two-dimensional space-time, where we show that the
formulation through Wilson fermions provides several advantages over the
previously considered staggered fermions. Notably, it enables a strongly
simplified optical lattice setup and it reduces the number of degrees of
freedom required to simulate dynamical gauge fields. Exploiting the optimal
representation, we propose an experiment based on a mixture of ultracold atoms
trapped in a tilted optical lattice. Using numerical benchmark simulations, we
demonstrate that a state-of-the-art quantum simulator may access the Schwinger
mechanism and map out its non-perturbative onset.Comment: 19 pages, 11 figure
Evolution equations for the effective four-quark interactions in QCD
A nonperturbative renormalization group equation describes how the momentum
dependent four-quark vertex depends on an infrared cutoff. We find a quasilocal
one-particle irreducible piece generated by (anomaly-free) multi-gluon
exchange. It becomes important at a cutoff scale where scalar and pseudoscalar
meson-bound states are expected to play a role. This interaction remains
subleading as compared to the effective one-gluon exchange contribution. The
local instanton induced four-quark interaction becomes dominant at a scale
around 800 MeV. In absence of a gluon mass the strong dependence of the
one-gluon exchange on the transferred momentum indicates that the pointlike
interactions of the Nambu-Jona-Lasinio model cannot give a very accurate
description of QCD. A pointlike effective four-quark interaction becomes more
realistic in case of spontaneous color symmetry breaking.Comment: 24 pages, LaTeX file, + 6 PS figure
Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
We uniquely determine the infrared asymptotics of Green functions in Landau
gauge Yang-Mills theory. They have to satisfy both,
Dyson-Schwinger equations and functional renormalisation group equations.
Then, consistency fixes the relation between the infrared power laws of these
Green functions. We discuss consequences for the interpretation of recent
results from lattice QCD.Comment: 24 pages, 8 figure
On supercorrelated systems and phase space entrainment
It is demonstrated that power-laws which are modified by logarithmic
corrections arise in supercorrelated systems. Their characteristic feature is
the energy attributed to a state (or value of a general cost function) which
depends nonlinearly on the phase space distribution of the constituents. A
onedimensional dissipative deterministic model is introduced which is attracted
to a supercorrelated state (phase space entrainment). Extensions of this
particular model may have applications in the study of transport and
equilibration phenomena, particularly for supply and information networks, or
for chemical and biological nonequilibrium systems, while the qualitative
arguments presented here are believed to be of more general interest.Comment: 12 pages - some technical material removed from second version,
several explanatory comments and references added instea
Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
We explore low temperature properties of quantum triangular Heisenberg
antiferromagnets in two dimension in the vicinity of the quantum phase
transition at zero temperature. Using the effective field theory described by
the matrix Ginzburg-Landau-Wilson model and the
non-perturbative renormalization group method, we clarify how quantum and
thermal fluctuations affect long-wavelength behaviors in the parameter region
where the systems exhibit a fluctuation-driven first order transition to a
long-range ordered state. We show that at finite temperatures the crossover
from a quantum theory to a renormalized two-dimensional classical
nonlinear sigma model region appears, and in this crossover region, massless
fluctuation modes with linear dispersion a la spin waves govern low-energy
physics. Our results are in good agreement with the recent experimental
observations for the two-dimensional triangular Heisenberg spin system,
NiGaS.Comment: 14 pages,7 figures, version accepted for publication in Physical
Review
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