645 research outputs found
Critical behavior of disordered systems with replica symmetry breaking
A field-theoretic description of the critical behavior of weakly disordered
systems with a -component order parameter is given. For systems of an
arbitrary dimension in the range from three to four, a renormalization group
analysis of the effective replica Hamiltonian of the model with an interaction
potential without replica symmetry is given in the two-loop approximation. For
the case of the one-step replica symmetry breaking, fixed points of the
renormalization group equations are found using the Pade-Borel summing
technique. For every value , the threshold dimensions of the system that
separate the regions of different types of the critical behavior are found by
analyzing those fixed points. Specific features of the critical behavior
determined by the replica symmetry breaking are described. The results are
compared with those obtained by the -expansion and the scope of the
method applicability is determined.Comment: 18 pages, 2 figure
Successful treatment of a solitary skull metastasis in a child with Wilms' Tumor
This report presents the successful treatment of a child with a solitary metastatic lesion to the calvarium following treatment for Stage III anaplastic Wilms’ Tumor
The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius
We consider a one-dimensional directed polymer in a random potential which is
characterized by the Gaussian statistics with the finite size local
correlations. It is shown that the well-known Kardar's solution obtained
originally for a directed polymer with delta-correlated random potential can be
applied for the description of the present system only in the high-temperature
limit. For the low temperature limit we have obtained the new solution which is
described by the one-step replica symmetry breaking. For the mean square
deviation of the directed polymer of the linear size L it provides the usual
scaling with the wandering exponent z = 2/3 and the
temperature-independent prefactor.Comment: 14 pages, Late
Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
A combination of recent numerical and theoretical advances are applied to
analyze the scaling behaviour of the site-diluted Ising model in two
dimensions, paying special attention to the implications for multiplicative
logarithmic corrections. The analysis focuses primarily on the odd sector of
the model (i.e., that associated with magnetic exponents), and in particular on
its Lee-Yang zeros, which are determined to high accuracy. Scaling relations
are used to connect to the even (thermal) sector, and a first analysis of the
density of zeros yields information on the specific heat and its corrections.
The analysis is fully supportive of the strong scaling hypothesis and of the
scaling relations for logarithmic corrections.Comment: 15 pages, 3 figures. Published versio
Coupled Ising models with disorder
In this paper we study the phase diagram of two Ising planes coupled by a
standard spin-spin interaction with bond randomness in each plane. The whole
phase diagram is analyzed by help of Monte Carlo simulations and field theory
arguments.Comment: 9 pages and 3 figure
Scaling Relations for Logarithmic Corrections
Multiplicative logarithmic corrections to scaling are frequently encountered
in the critical behavior of certain statistical-mechanical systems. Here, a
Lee-Yang zero approach is used to systematically analyse the exponents of such
logarithms and to propose scaling relations between them. These proposed
relations are then confronted with a variety of results from the literature.Comment: 4 page
Surface critical behavior of two-dimensional dilute Ising models
Ising models with nearest-neighbor ferromagnetic random couplings on a square
lattice with a (1,1) surface are studied, using Monte Carlo techniques and
star-tiangle transformation method. In particular, the critical exponent of the
surface magnetization is found to be close to that of the perfect model,
beta_s=1/2. The crossover from surface to bulk critical properties is
discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy
Logarithmic corrections in the two-dimensional Ising model in a random surface field
In the two-dimensional Ising model weak random surface field is predicted to
be a marginally irrelevant perturbation at the critical point. We study this
question by extensive Monte Carlo simulations for various strength of disorder.
The calculated effective (temperature or size dependent) critical exponents fit
with the field-theoretical results and can be interpreted in terms of the
predicted logarithmic corrections to the pure system's critical behaviour.Comment: 10 pages, 4 figures, extended version with one new sectio
Boundary critical behaviour of two-dimensional random Ising models
Using Monte Carlo techniques and a star-triangle transformation, Ising models
with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on
a square lattice with a (1,1) surface are studied near the phase transition.
Both surface and bulk critical properties are investigated. In particular, the
critical exponents of the surface magnetization, 'beta_1', of the correlation
length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are
analysed.Comment: 16 pages in ioplppt style, 7 ps figures, submitted to J. Phys.
Logarithmic corrections to gap scaling in random-bond Ising strips
Numerical results for the first gap of the Lyapunov spectrum of the self-dual
random-bond Ising model on strips are analysed. It is shown that finite-width
corrections can be fitted very well by an inverse logarithmic form, predicted
to hold when the Hamiltonian contains a marginal operator.Comment: LaTeX code with Institute of Physics macros for 7 pages, plus 2
Postscript figures; to appear in Journal of Physics A (Letter to the Editor
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