70 research outputs found
High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions
In order to study the influence of quenched disorder on second-order phase
transitions, high-temperature series expansions of the \sus and the free energy
are obtained for the quenched bond-diluted Ising model in --5
dimensions. They are analysed using different extrapolation methods tailored to
the expected singularity behaviours. In and 5 dimensions we confirm
that the critical behaviour is governed by the pure fixed point up to dilutions
near the geometric bond percolation threshold. The existence and form of
logarithmic corrections for the pure Ising model in is confirmed and
our results for the critical behaviour of the diluted system are in agreement
with the type of singularity predicted by renormalization group considerations.
In three dimensions we find large crossover effects between the pure Ising,
percolation and random fixed point. We estimate the critical exponent of the
\sus to be at the random fixed point.Comment: 16 pages, 10 figure
Universality class of 3D site-diluted and bond-diluted Ising systems
We present a finite-size scaling analysis of high-statistics Monte Carlo
simulations of the three-dimensional randomly site-diluted and bond-diluted
Ising model. The critical behavior of these systems is affected by
slowly-decaying scaling corrections which make the accurate determination of
their universal asymptotic behavior quite hard, requiring an effective control
of the scaling corrections. For this purpose we exploit improved Hamiltonians,
for which the leading scaling corrections are suppressed for any thermodynamic
quantity, and improved observables, for which the leading scaling corrections
are suppressed for any model belonging to the same universality class.
The results of the finite-size scaling analysis provide strong numerical
evidence that phase transitions in three-dimensional randomly site-diluted and
bond-diluted Ising models belong to the same randomly dilute Ising universality
class. We obtain accurate estimates of the critical exponents, ,
, , , ,
, and of the leading and next-to-leading correction-to-scaling
exponents, and .Comment: 45 pages, 22 figs, revised estimate of n
Star-graph expansions for bond-diluted Potts models
We derive high-temperature series expansions for the free energy and the
susceptibility of random-bond -state Potts models on hypercubic lattices
using a star-graph expansion technique. This method enables the exact
calculation of quenched disorder averages for arbitrary uncorrelated coupling
distributions. Moreover, we can keep the disorder strength as well as the
dimension as symbolic parameters. By applying several series analysis
techniques to the new series expansions, one can scan large regions of the
parameter space for any value of . For the bond-diluted 4-state
Potts model in three dimensions, which exhibits a rather strong first-order
phase transition in the undiluted case, we present results for the transition
temperature and the effective critical exponent as a function of
as obtained from the analysis of susceptibility series up to order 18. A
comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev.
E64, 036120(2001)) shows signals for the softening to a second-order transition
at finite disorder strength.Comment: 8 pages, 6 figure
Unpolarized quasielectrons and the spin polarization at filling fractions between 1/3 and 2/5
We prove that for a hard core interaction the ground state spin polarization
in the low Zeeman energy limit is given by for filling fractions in
the range . The same result holds for a Coulomb
potential except for marginally small magnetic fields. At the magnetic fields
unpolarized quasielectrons can manifest themselves by a characteristic
peak in the I-V characteristics for tunneling between two
ferromagnets.Comment: 8 pages, Latex. accepted for publication in Phys.Rev.
Static solitons with non-zero Hopf number
We investigate a generalized non-linear O(3) -model in three space
dimensions where the fields are maps . Such maps are
classified by a homotopy invariant called the Hopf number which takes integer
values. The model exhibits soliton solutions of closed vortex type which have a
lower topological bound on their energies. We explicitly compute the fields for
topological charge 1 and 2 and discuss their shapes and binding energies. The
effect of an additional potential term is considered and an approximation is
given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made,
a reference has been corrected and a figure replace
Spontaneous annihilation of high-density matter in the electroweak theory
In the presence of fermionic matter the topologically distinct vacua of the
standard model are metastable and can decay by tunneling through the sphaleron
barrier. This process annihilates one fermion per doublet due to the anomalous
non-conservation of baryon and lepton currents and is accompanied by a
production of gauge and Higgs bosons. We present a numerical method to obtain
local bounce solutions which minimize the Euclidean action in the space of all
configurations connecting two adjacent topological sectors. These solutions
determine the decay rate and the configuration of the fields after the
tunneling. We also follow the real time evolution of this configuration and
analyze the spectrum of the created bosons. If the matter density exceeds some
critical value, the exponentially suppressed tunneling triggers off an
avalanche producing an enormous amount of bosons.Comment: 38 pages, 6 Postscript figure
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
Fluctuation corrections to bubble nucleation
The fluctuation determinant which determines the preexponential factor of the
transition rate for minimal bubbles is computed for the electroweak theory with
. As the basic action we use the three-dimensional
high-temperature action including, besides temperature dependent masses, the one-loop contribution which makes the phase transition first order. The
results show that this contribution (which has then to be subtracted from the
exact result) gives the dominant contribution to the one-loop effective action.
The remaining correction is of the order of, but in general larger than the
critical bubble action and suppresses the transition rate. The results for the
Higgs field fluctuations are compared with those of an approximate heat kernel
computation of Kripfganz et al., good agreement is found for small bubbles,
strong deviations for large thin-wall bubbles.Comment: 19 pages, LaTeX, no macros, no figure
One-loop corrections to the metastable vacuum decay
We evaluate the one-loop prefactor in the false vacuum decay rate in a theory
of a self interacting scalar field in 3+1 dimensions. We use a numerical
method, established some time ago, which is based on a well-known theorem on
functional determinants. The proper handling of zero modes and of
renormalization is discussed. The numerical results in particular show that
quantum corrections become smaller away from the thin-wall case. In the
thin-wall limit the numerical results are found to join into those obtained by
a gradient expansion.Comment: 31 pages, 7 figure
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