4,504 research outputs found
Critical behaviour of the two-dimensional Ising susceptibility
We report computations of the short-distance and the long-distance (scaling)
contributions to the square-lattice Ising susceptibility in zero field close to
T_c. Both computations rely on the use of nonlinear partial difference
equations for the correlation functions. By summing the correlation functions,
we give an algorithm of complexity O(N^6) for the determination of the first N
series coefficients. Consequently, we have generated and analysed series of
length several hundred terms, generated in about 100 hours on an obsolete
workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the
short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2.
To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4}
singularity contains only integer powers of \tau. The presence of irrelevant
variables in the scaling function is clearly evident, with contributions of
distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being
identified.Comment: 11 pages, REVTex
On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture
We show that for an odd prime p, the p-primary parts of refinements of the
(imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by
the equivariant Iwasawa main conjecture (EIMC) for totally real fields.
Crucially, this result does not depend on the vanishing of the relevant Iwasawa
mu-invariant. In combination with the authors' previous work on the EIMC, this
leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark
conjectures in many new cases.Comment: 33 pages; to appear in Mathematische Zeitschrift; v3 many minor
updates including new title; v2 some cohomological arguments simplified; v1
is a revised version of the second half of arXiv:1408.4934v
Bullying girls - Changes after brief strategic family therapy: A randomized, prospective, controlled trial with one-year follow-up
Background: Many girls bully others. They are conspicuous because of their risk-taking behavior, increased anger, problematic interpersonal relationships and poor quality of life. Our aim was to determine the efficacy of brief strategic family therapy (BSFT) for bullying-related behavior, anger reduction, improvement of interpersonal relationships, and improvement of health-related quality of life in girls who bully, and to find out whether their expressive aggression correlates with their distinctive psychological features. Methods: 40 bullying girls were recruited from the general population: 20 were randomly selected for 3 months of BSFT. Follow-up took place 12 months after the therapy had ended. The results of treatment were examined using the Adolescents' Risk-taking Behavior Scale (ARBS), the State-Trait Anger Expression Inventory (STAXI), the Inventory of Interpersonal Problems (IIP-D), and the SF-36 Health Survey (SF-36). Results: In comparison with the control group (CG) (according to the intent-to-treat principle), bullying behavior in the BSFT group was reduced (BSFT-G from n = 20 to n = 6; CG from n = 20 to n = 18, p = 0.05) and statistically significant changes in all risk-taking behaviors (ARBS), on most STAXI, IIP-D, and SF-36 scales were observed after BSFT. The reduction in expressive aggression (Anger-Out scale of the STAXI) correlated with the reduction on several scales of the ARBS, IIP-D, and SF-36. Follow-up a year later showed relatively stable events. Conclusions: Our findings suggest that bullying girls suffer from psychological and social problems which may be reduced by the use of BSFT. Expressive aggression in girls appears to correlate with several types of risk-taking behavior and interpersonal problems, as well as with health-related quality of life. Copyright (c) 2006 S. Karger AG, Basel
Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point
We compute the non--trivial infrared --fixed point by means of an
interpolation expansion in fixed dimension. The expansion is formulated for an
infinitesimal momentum space renormalization group. We choose a coordinate
representation for the fixed point interaction in derivative expansion, and
compute its coordinates to high orders by means of computer algebra. We compute
the series for the critical exponent up to order twenty five of
interpolation expansion in this representation, and evaluate it using \pade,
Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The
resummation returns as the value of .Comment: 29 pages, Latex2e, 2 Postscript figure
Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
We calculate very long low- and high-temperature series for the
susceptibility of the square lattice Ising model as well as very long
series for the five-particle contribution and six-particle
contribution . These calculations have been made possible by the
use of highly optimized polynomial time modular algorithms and a total of more
than 150000 CPU hours on computer clusters. For 10000 terms of the
series are calculated {\it modulo} a single prime, and have been used to find
the linear ODE satisfied by {\it modulo} a prime.
A diff-Pad\'e analysis of 2000 terms series for and
confirms to a very high degree of confidence previous conjectures about the
location and strength of the singularities of the -particle components of
the susceptibility, up to a small set of ``additional'' singularities. We find
the presence of singularities at for the linear ODE of ,
and for the ODE of , which are {\it not} singularities
of the ``physical'' and that is to say the
series-solutions of the ODE's which are analytic at .
Furthermore, analysis of the long series for (and )
combined with the corresponding long series for the full susceptibility
yields previously conjectured singularities in some , .
We also present a mechanism of resummation of the logarithmic singularities
of the leading to the known power-law critical behaviour occurring
in the full , and perform a power spectrum analysis giving strong
arguments in favor of the existence of a natural boundary for the full
susceptibility .Comment: 54 pages, 2 figure
The diagonal Ising susceptibility
We use the recently derived form factor expansions of the diagonal two-point
correlation function of the square Ising model to study the susceptibility for
a magnetic field applied only to one diagonal of the lattice, for the isotropic
Ising model.
We exactly evaluate the one and two particle contributions
and of the corresponding susceptibility, and obtain linear
differential equations for the three and four particle contributions, as well
as the five particle contribution , but only modulo a given
prime. We use these exact linear differential equations to show that, not only
the russian-doll structure, but also the direct sum structure on the linear
differential operators for the -particle contributions are
quite directly inherited from the direct sum structure on the form factors .
We show that the particle contributions have their
singularities at roots of unity. These singularities become dense on the unit
circle as .Comment: 18 page
The Magnetization of the 3D Ising Model
We present highly accurate Monte Carlo results for simple cubic Ising
lattices containing up to spins. These results were obtained by means
of the Cluster Processor, a newly built special-purpose computer for the Wolff
cluster simulation of the 3D Ising model. We find that the magnetization
is perfectly described by , where
, in a wide temperature range .
If there exist corrections to scaling with higher powers of , they are very
small. The magnetization exponent is determined as (6). An
analysis of the magnetization distribution near criticality yields a new
determination of the critical point: ,
with a standard deviation of .Comment: 7 pages, 5 Postscript figure
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