42 research outputs found
A massive Feynman integral and some reduction relations for Appell functions
New explicit expressions are derived for the one-loop two-point Feynman
integral with arbitrary external momentum and masses and in D
dimensions. The results are given in terms of Appell functions, manifestly
symmetric with respect to the masses . Equating our expressions with
previously known results in terms of Gauss hypergeometric functions yields
reduction relations for the involved Appell functions that are apparently new
mathematical results.Comment: 19 pages. To appear in Journal of Mathematical Physic
Large-n expansion for m-axial Lifshitz points
The large-n expansion is developed for the study of critical behaviour of
d-dimensional systems at m-axial Lifshitz points with an arbitrary number m of
modulation axes. The leading non-trivial contributions of O(1/n) are derived
for the two independent correlation exponents \eta_{L2} and \eta_{L4}, and the
related anisotropy index \theta. The series coefficients of these 1/n
corrections are given for general values of m and d with 0<m<d and
2+m/2<d<4+m/2 in the form of integrals. For special values of m and d such as
(m,d)=(1,4), they can be computed analytically, but in general their evaluation
requires numerical means. The 1/n corrections are shown to reduce in the
appropriate limits to those of known large-n expansions for the case of
d-dimensional isotropic Lifshitz points and critical points, respectively, and
to be in conformity with available dimensionality expansions about the upper
and lower critical dimensions. Numerical results for the 1/n coefficients of
\eta_{L2}, \eta_{L4} and \theta are presented for the physically interesting
case of a uniaxial Lifshitz point in three dimensions, as well as for some
other choices of m and d. A universal coefficient associated with the
energy-density pair correlation function is calculated to leading order in 1/n
for general values of m and d.Comment: 28 pages, 3 figures. Submitted to: J. Phys. C: Solid State Phys.,
special issue dedicated to Lothar Schaefer on the occasion of his 60th
birthday. V2: References added along with corresponding modifications in the
text, corrected figure 3, corrected typo
Compatibility of 1/n and epsilon expansions for critical exponents at m-axial Lifshitz points
The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz
points is considered for general values of m in the large-n limit. It is proven
that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17,
S1947 (2005)] of the correlation exponents \eta_{L2}, \eta_{L4} and the related
anisotropy exponent \theta are fully consistent with the dimensionality
expansions to second order in \epsilon=4+m/2-d [Phys. Rev. B 62, 12338 (2000);
Nucl. Phys. B 612, 340 (2001)] inasmuch as both expansions yield the same
contributions of order \epsilon^2/n.Comment: 8 pages, submitted to J. Phys.
Influence of long-range correlated quenched disorder on the adsorption of long flexible polymer chains on a wall
The process of adsorption on a planar wall of long-flexible polymer chains in
the medium with quenched long-range correlated disorder is investigated. We
focus on the case of correlations between defects or impurities that decay
according to the power-low for large distances , where . Field theoretical approach in and directly in
dimensions up to one-loop order for the semi-infinite m-vector
model (in the limit ) with a planar boundary is used. The whole set of
surface critical exponents at the adsorption threshold , which separates
the nonadsorbed region from the adsorbed one is obtained. Moreover, we
calculate the crossover critical exponent and the set of exponents
associated with them. We perform calculations in a double and
expansion and also for a fixed dimension , up to one-loop
order for different values of the correlation parameter .
The obtained results indicate that for the systems with long-range correlated
quenched disorder the new set of surface critical exponents arises. All the
surface critical exponents depend on . Hence, the presence of long-range
correlated disorder influences the process of adsorption of long-flexible
polymer chains on a wall in a significant way.Comment: 4 figures, 2 table
Surface critical behavior of random systems at the ordinary transition
We calculate the surface critical exponents of the ordinary transition
occuring in semi-infinite, quenched dilute Ising-like systems. This is done by
applying the field theoretic approach directly in d=3 dimensions up to the
two-loop approximation, as well as in dimensions. At
we extend, up to the next-to-leading order, the previous
first-order results of the expansion by Ohno and Okabe
[Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface
exponents are computed using Pade approximants extrapolating the perturbation
theory expansions. The obtained results indicate that the critical behavior of
semi-infinite systems with quenched bulk disorder is characterized by the new
set of surface critical exponents.Comment: 11 pages, 11 figure