831 research outputs found
Correlations in Ising chains with non-integrable interactions
Two-spin correlations generated by interactions which decay with distance r
as r^{-1-sigma} with -1 <sigma <0 are calculated for periodic Ising chains of
length L. Mean-field theory indicates that the correlations, C(r,L), diminish
in the thermodynamic limit L -> \infty, but they contain a singular structure
for r/L -> 0 which can be observed by introducing magnified correlations,
LC(r,L)-\sum_r C(r,L). The magnified correlations are shown to have a scaling
form F(r/L) and the singular structure of F(x) for x->0 is found to be the same
at all temperatures including the critical point. These conclusions are
supported by the results of Monte Carlo simulations for systems with sigma
=-0.50 and -0.25 both at the critical temperature T=Tc and at T=2Tc.Comment: 13 pages, latex, 5 eps figures in a separate uuencoded file, to
appear in Phys.Rev.
Flow Equations for U_k and Z_k
By considering the gradient expansion for the wilsonian effective action S_k
of a single component scalar field theory truncated to the first two terms, the
potential U_k and the kinetic term Z_k, I show that the recent claim that
different expansion of the fluctuation determinant give rise to different
renormalization group equations for Z_k is incorrect. The correct procedure to
derive this equation is presented and the set of coupled differential equations
for U_k and Z_k is definitely established.Comment: 5 page
Statistics of Lyapunov exponent in one-dimensional layered systems
Localization of acoustic waves in a one dimensional water duct containing
many randomly distributed air filled blocks is studied. Both the Lyapunov
exponent and its variance are computed. Their statistical properties are also
explored extensively. The results reveal that in this system the single
parameter scaling is generally inadequate no matter whether the frequency we
consider is located in a pass band or in a band gap. This contradicts the
earlier observations in an optical case. We compare the results with two
optical cases and give a possible explanation of the origin of the different
behaviors.Comment: 6 pages revtex file, 6 eps figure
On stability of the three-dimensional fixed point in a model with three coupling constants from the expansion: Three-loop results
The structure of the renormalization-group flows in a model with three
quartic coupling constants is studied within the -expansion method up
to three-loop order. Twofold degeneracy of the eigenvalue exponents for the
three-dimensionally stable fixed point is observed and the possibility for
powers in to appear in the series is investigated.
Reliability and effectiveness of the -expansion method for the given
model is discussed.Comment: 14 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57
(1998
Medium-range interactions and crossover to classical critical behavior
We study the crossover from Ising-like to classical critical behavior as a
function of the range R of interactions. The power-law dependence on R of
several critical amplitudes is calculated from renormalization theory. The
results confirm the predictions of Mon and Binder, which were obtained from
phenomenological scaling arguments. In addition, we calculate the range
dependence of several corrections to scaling. We have tested the results in
Monte Carlo simulations of two-dimensional systems with an extended range of
interaction. An efficient Monte Carlo algorithm enabled us to carry out
simulations for sufficiently large values of R, so that the theoretical
predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available
as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm
Driven diffusive system with non-local perturbations
We investigate the impact of non-local perturbations on driven diffusive
systems. Two different problems are considered here. In one case, we introduce
a non-local particle conservation along the direction of the drive and in
another case, we incorporate a long-range temporal correlation in the noise
present in the equation of motion. The effect of these perturbations on the
anisotropy exponent or on the scaling of the two-point correlation function is
studied using renormalization group analysis.Comment: 11 pages, 2 figure
On critical behavior of phase transitions in certain antiferromagnets with complicated ordering
Within the four-loop \ve expansion, we study the critical behavior of
certain antiferromagnets with complicated ordering. We show that an anisotropic
stable fixed point governs the phase transitions with new critical exponents.
This is supported by the estimate of critical dimensionality
obtained from six loops via the exact relation established
for the real and complex hypercubic models.Comment: Published versio
Random Walks with Long-Range Self-Repulsion on Proper Time
We introduce a model of self-repelling random walks where the short-range
interaction between two elements of the chain decreases as a power of the
difference in proper time. Analytic results on the exponent are obtained.
They are in good agreement with Monte Carlo simulations in two dimensions. A
numerical study of the scaling functions and of the efficiency of the algorithm
is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included)
IFUP-Th 13/92 and SNS 14/9
Propagation of a hole on a Neel background
We analyze the motion of a single hole on a N\'eel background, neglecting
spin fluctuations. Brinkman and Rice studied this problem on a cubic lattice,
introducing the retraceable-path approximation for the hole Green's function,
exact in a one-dimensional lattice. Metzner et al. showed that the
approximationalso becomes exact in the infinite-dimensional limit. We introduce
a new approach to this problem by resumming the Nagaoka expansion of the
propagator in terms of non-retraceable skeleton-paths dressed by
retraceable-path insertions. This resummation opens the way to an almost
quantitative solution of the problemin all dimensions and, in particular sheds
new light on the question of the position of the band-edges. We studied the
motion of the hole on a double chain and a square lattice, for which deviations
from the retraceable-path approximation are expected to be most pronounced. The
density of states is mostly adequately accounted for by the
retra\-ce\-able-path approximation. Our band-edge determination points towards
an absence of band tails extending to the Nagaoka energy in the spectrums of
the double chain and the square lattice. We also evaluated the spectral density
and the self-energy, exhibiting k-dependence due to finite dimensionality. We
find good agreement with recent numerical results obtained by Sorella et al.
with the Lanczos spectra decoding method. The method we employ enables us to
identify the hole paths which are responsible for the various features present
in the density of states and the spectral density.Comment: 26 pages,Revte
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