109 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
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
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
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