5,426 research outputs found
The four-loop DRED gauge beta-function and fermion mass anomalous dimension for general gauge groups
We present four-loop results for the gauge beta-function and the fermion mass
anomalous dimension for a gauge theory with a general gauge group and a
multiplet of fermions transforming according to an arbitrary representation,
calculated using the dimensional reduction scheme. In the special case of a
supersymmetric theory we confirm previous calculations of both the gauge
beta-function and the gaugino mass beta-function.Comment: 44 pages, added references (v2) minor changes (v3
Planar Octilinear Drawings with One Bend Per Edge
In octilinear drawings of planar graphs, every edge is drawn as an
alternating sequence of horizontal, vertical and diagonal ()
line-segments. In this paper, we study octilinear drawings of low edge
complexity, i.e., with few bends per edge. A -planar graph is a planar graph
in which each vertex has degree less or equal to . In particular, we prove
that every 4-planar graph admits a planar octilinear drawing with at most one
bend per edge on an integer grid of size . For 5-planar
graphs, we prove that one bend per edge still suffices in order to construct
planar octilinear drawings, but in super-polynomial area. However, for 6-planar
graphs we give a class of graphs whose planar octilinear drawings require at
least two bends per edge
Strictly convex drawings of planar graphs
Every three-connected planar graph with n vertices has a drawing on an O(n^2)
x O(n^2) grid in which all faces are strictly convex polygons. These drawings
are obtained by perturbing (not strictly) convex drawings on O(n) x O(n) grids.
More generally, a strictly convex drawing exists on a grid of size O(W) x
O(n^4/W), for any choice of a parameter W in the range n<W<n^2. Tighter bounds
are obtained when the faces have fewer sides.
In the proof, we derive an explicit lower bound on the number of primitive
vectors in a triangle.Comment: 20 pages, 13 figures. to be published in Documenta Mathematica. The
revision includes numerous small additions, corrections, and improvements, in
particular: - a discussion of the constants in the O-notation, after the
statement of thm.1. - a different set-up and clarification of the case
distinction for Lemma
Optical conductivity in multiferroic GaVS and GeVS: Phonons and electronic transitions
We report on optical spectroscopy on the lacunar spinels GaVS and
GeVS in the spectral range from 100 to 23000 cm and for
temperatures from 5 to 300 K. These multiferroic spinel systems reveal
Jahn-Teller driven ferroelectricity and complex magnetic order at low
temperatures. We study the infrared-active phonon modes and the low-lying
electronic excitations in the cubic high-temperature phase, as well as in the
orbitally and in the magnetically ordered low-temperature phases. We compare
the phonon modes in these two compounds, which undergo different
symmetry-lowering Jahn-Teller transitions into ferroelectric and orbitally
ordered phases, and exhibit different magnetic ground states. We follow the
splitting of the phonon modes at the structural phase transition and detect
additional splittings at the onset of antiferromagnetic order in GeVS.
We observe electronic transitions within the -derived bands of the V
clusters and document a significant influence of the structural and magnetic
phase transitions on the narrow electronic band gaps.Comment: 12 pages, 10 figure
Polar Dynamics at the Jahn-Teller Transition in Ferroelectric GaV4S8
We present a dielectric spectroscopy study of the polar dynamics linked to
the orbitally driven ferroelectric transition in the skyrmion host GaV4S8. By
combining THz and MHz-GHz spectroscopy techniques, we succeed in detecting the
relaxational dynamics arising from coupled orbital and polar fluctuations in
this material and traced its temperature dependence in the paraelectric as well
as in the ferroelectric phase. The relaxation time significantly increases when
approaching the critical temperature from both sides of the transition. It is
natural to assume that these polar fluctuations map the orbital dynamics at the
Jahn-Teller transition. Due to the first-order character of the
orbital-ordering transition, the relaxation time shows an enormous jump of
about five orders of magnitude at the polar and structural phase transition.Comment: 5 pages, 4 figure
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