98 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
Interaction dependence of composite fermion effective masses
We estimate the composite fermion effective mass for a general two particle
potential r^{-\alpha} using exact diagonalization for polarized electrons in
the lowest Landau level on a sphere. Our data for the ground state energy at
filling fraction \nu=1/2 as well as estimates of the excitation gap at \nu=1/3,
2/5 and 3/7 show that m_eff \sim \alpha^{-1}.Comment: 4 pages, RevTeX, 5 figure
Symmetric polynomials in information theory: Entropy and subentropy
Entropy and other fundamental quantities of information theory are customarily
expressed and manipulated as functions of probabilities. Here we study the entropy H
and subentropy Q as functions of the elementary symmetric polynomials in the probabilities,
and reveal a series of remarkable properties. Derivatives of all orders are shown
to satisfy a complete monotonicity property. H and Q themselves become multivariate
Bernstein functions and we derive the density functions of their Levy-Khintchine
representations. We also show that H and Q are Pick functions in each symmetric
polynomial variable separately. Furthermore we see that H and the intrinsically quantum
informational quantity Q become surprisingly closely related in functional form,
suggesting a special signi cance for the symmetric polynomials in quantum information
theory. Using the symmetric polynomials we also derive a series of further properties
of H and Q.This is the accepted manuscript. The final version is available at http://scitation.aip.org/content/aip/journal/jmp/56/6/10.1063/1.4922317
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
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.
Prompt Quark Production by exploding Sphalerons
Following recent works on production and subsequent explosive decay of QCD
sphaleron-like clusters, we discuss the mechanism of quark pair production in
this process. We first show how the gauge field explosive solution of Luscher
and Schechter can be achieved by non-central conformal mapping from the
O(4)-symmetric solution. Our main result is a new solution to the Dirac
equation in real time in this configuration, obtained by the same inversion of
the fermion O(4) zero mode. It explicitly shows how the quark acceleration
occurs, starting from the spherically O(3) symmetric zero energy chiral quark
state to the final spectrum of non-zero energies.
The sphaleron-like clusters with any Chern-Simons number always produce quarks, and the antisphaleron-like clusters the
chirality opposite.
The result are relevant for hadron-hadron and nucleus-nucleus collisions at
large , wherein such clusters can be produced
Prompt Multi-Gluon Production in High Energy Collisions from Singular Yang-Mills Solutions
We study non-perturbative parton-parton scattering in the Landau method using
singular O(3) symmetric solutions to the Euclidean Yang-Mills equations. These
solutions combine instanton dynamics (tunneling) and overlap (transition)
between incoming and vacuum fields. We derive a high-energy solution at small
Euclidean times, and assess its susequent escape and decay into gluons in
Minkowski space-time. We describe the spectrum of the {\it outgoing} gluons and
show that it is related through a particular rescaling to the Yang-Mills
sphaleron explosion studied earlier. We assess the number of {\it incoming}
gluons in the same configuration, and argue that the observed scaling is in
fact more general and describes the energy dependence of the spectra and
multiplicities at {\it all} energies. Applications to hadron-hadron and
nucleus-nucleus collisions are discussed elsewhere
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
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