20 research outputs found
Topography of the hot sphaleron Transitions
By numerical simulations in {\it real time} we provide evidence in favour of
sphaleron like transitions in the hot, symmetric phase of the electroweak
theory. Earlier performed observations of a change in the Chern-Simons number
are supplemented with a measurement of the lowest eigenvalues of the
three-dimensional staggered fermion Dirac operator and observations of the
spatial extension of energy lumps associated with the transition. The
observations corroborate on the interpretation of the change in Chern-Simons
numbers as representing continuum physics, not lattice artifacts. By combining
the various observations it is possible to follow in considerable detail the
time-history of thermal fluctuations of the classical gauge-field
configurations responsible for the change in the Chern-Simons number.Comment: 11 pages. No figures (sorry, but ps files too huge). Latex file.
NBI-HE-92-5
Grand-Canonical Ensemble of Random Surfaces with Four Species of Ising Spins
The grand-canonical ensemble of dynamically triangulated surfaces coupled to
four species of Ising spins (c=2) is simulated on a computer. The effective
string susceptibility exponent for lattices with up to 1000 vertices is found
to be . A specific scenario for models is
conjectured.Comment: LaTeX, 11 pages + 1 postscript figure appended, preprint LPTHE-Orsay
94/1
On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity
We have studied a model which has been proposed as a regularisation for four
dimensional quantum gravity. The partition function is constructed by
performing a weighted sum over all triangulations of the four sphere. Using
numerical simulation we find that the number of such triangulations containing
simplices grows faster than exponentially with . This property ensures
that the model has no thermodynamic limit.Comment: 8 pages, 2 figure
Ising-link Quantum Gravity
We define a simplified version of Regge quantum gravity where the link
lengths can take on only two possible values, both always compatible with the
triangle inequalities. This is therefore equivalent to a model of Ising spins
living on the links of a regular lattice with somewhat complicated, yet local
interactions. The measure corresponds to the natural sum over all 2^links
configurations, and numerical simulations can be efficiently implemented by
means of look-up tables. In three dimensions we find a peak in the ``curvature
susceptibility'' which grows with increasing system size. However, the value of
the corresponding critical exponent as well as the behavior of the curvature at
the transition differ from that found by Hamber and Williams for the Regge
theory with continuously varying link lengths.Comment: 11 page
A Lorentzian cure for Euclidean troubles
There is strong evidence coming from Lorentzian dynamical triangulations that
the unboundedness of the gravitational action is no obstacle to the
construction of a well-defined non-perturbative path integral. In a continuum
approach, a similar suppression of the conformal divergence comes about as the
result of a non-trivial path-integral measure.Comment: 3 page
Generalized Penner models to all genera
We give a complete description of the genus expansion of the one-cut solution
to the generalized Penner model. The solution is presented in a form which
allows us in a very straightforward manner to localize critical points and to
investigate the scaling behaviour of the model in the vicinity of these points.
We carry out an analysis of the critical behaviour to all genera addressing all
types of multi-critical points. In certain regions of the coupling constant
space the model must be defined via analytical continuation. We show in detail
how this works for the Penner model. Using analytical continuation it is
possible to reach the fermionic 1-matrix model. We show that the critical
points of the fermionic 1-matrix model can be indexed by an integer, , as it
was the case for the ordinary hermitian 1-matrix model. Furthermore the 'th
multi-critical fermionic model has to all genera the same value of
as the 'th multi-critical hermitian model. However, the
coefficients of the topological expansion need not be the same in the two
cases. We show explicitly how it is possible with a fermionic matrix model to
reach a multi-critical point for which the topological expansion has
alternating signs, but otherwise coincides with the usual Painlev\'{e}
expansion.Comment: 27 pages, PostScrip
The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory
The vacuum effective potential of three-dimensional SU(2) lattice gauge
theory in an applied color-magnetic field is computed over a wide range of
field strengths. The background field is induced by an external current, as in
continuum field theory. Scaling and finite volume effects are analyzed
systematically. The first evidence from lattice simulations is obtained of the
existence of a nontrivial minimum in the effective potential. This supports a
``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the
basis of a one-loop calculation in (3+1)-dimensional QCD.Comment: 9pp (REVTEX manuscript). Postscript figures appende
Universal correlations for deterministic plus random Hamiltonians
We consider the (smoothed) average correlation between the density of energy
levels of a disordered system, in which the Hamiltonian is equal to the sum of
a deterministic H0 and of a random potential . Remarkably, this
correlation function may be explicitly determined in the limit of large
matrices, for any unperturbed H0 and for a class of probability distribution
P of the random potential. We find a compact representation of the
correlation function. From this representation one obtains readily the short
distance behavior, which has been conjectured in various contexts to be
universal. Indeed we find that it is totally independent of both H0 and
P().Comment: 26P, (+5 figures not included
Two-dimensional gravitation and Sine-Gordon-Solitons
Some aspects of two-dimensional gravity coupled to matter fields, especially
to the Sine-Gordon-model are examined. General properties and boundary
conditions of possible soliton-solutions are considered. Analytic
soliton-solutions are discovered and the structure of the induced space-time
geometry is discussed. These solutions have interesting features and may serve
as a starting point for further investigations.Comment: 23 pages, latex, references added, to appear in Phys.Rev.
On the stability of renormalizable expansions in three-dimensional gravity
Preliminary investigations are made for the stability of the expansion
in three-dimensional gravity coupled to various matter fields, which are
power-counting renormalizable. For unitary matters, a tachyonic pole appears in
the spin-2 part of the leading graviton propagator, which implies the unstable
flat space-time, unless the higher-derivative terms are introduced. As another
possibility to avoid this spin-2 tachyon, we propose Einstein gravity coupled
to non-unitary matters. It turns out that a tachyon appears in the spin-0 or -1
part for any linear gauges in this case, but it can be removed if non-minimally
coupled scalars are included. We suggest an interesting model which may be
stable and possess an ultraviolet fixed point.Comment: 32 pages. (A further discussion to avoid tachyons is included. To be
Published in Physical Review D.