155 research outputs found
Universal sextic effective interaction at criticality
The renormalization group approach in three dimensions is used to estimate
the universal critical value g_6^* of the dimensionless sextic effective
coupling constant for the Ising model. The four-loop RG expansion for g_6 is
calculated and resummed by means of the Pade-Borel and Pade-Borel-Leroy
procedures resulting in g_6^* = 1.596, while the most accurate estimate for
g_6^* is argued to be equal to 1.61.Comment: 6 pages, TeX, no figure
Towards deterministic equations for Levy walks: the fractional material derivative
Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited
Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
The renormalization-group (RG) functions for the three-dimensional n-vector
cubic model are calculated in the five-loop approximation. High-precision
numerical estimates for the asymptotic critical exponents of the
three-dimensional impure Ising systems are extracted from the five-loop RG
series by means of the Pade-Borel-Leroy resummation under n = 0. These
exponents are found to be: \gamma = 1.325 +/- 0.003, \eta = 0.025 +/- 0.01, \nu
= 0.671 +/- 0.005, \alpha = - 0.0125 +/- 0.008, \beta = 0.344 +/- 0.006. For
the correction-to-scaling exponent, the less accurate estimate \omega = 0.32
+/- 0.06 is obtained.Comment: 11 pages, LaTeX, no figures, published versio
Strong decays and dipion transitions of Upsilon(5S)
Dipion transitions of with are studied using
the Field Correlator Method, applied previously to dipion transitions with
The only two parameters of effective Lagrangian were fixed in that
earlier study, and total widths as well as pionless
decay widths and
were calculated and are in a reasonable agreement with
experiment. The experimental spectra for and (5,2) transitions
are well reproduced taking into account FSI in the .Comment: 16 pages, 6 figure
Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation
The critical behavior of the two-dimensional N-vector cubic model is studied
within the field-theoretical renormalization-group (RG) approach. The
β functions and critical exponents are calculated in the five-loop approximation,
RG series obtained are resummed using Pade-Borel-Leroy and ´
conformal mapping techniques. It is found that for N = 2 the continuous
line of fixed points is well reproduced by the resummed RG series and an
account for the five-loop terms makes the lines of zeros of both β functions
closer to each other. For N > 3 the five-loop contributions are shown to
shift the cubic fixed point, given by the four-loop approximation, towards
the Ising fixed point. This confirms the idea that the existence of the cubic
fixed point in two dimensions under N >2 is an artifact of the perturbative
analysis. In the case N = 0 the results obtained are compatible with the
conclusion that the impure critical behavior is controlled by the Ising fixed
point.В рамках теоретико-польового підходу ренормалізаційної групи (РГ)
вивчається критична поведінка двовимірної N-векторної кубічної
моделі. β функції і критичні показники обчислюються в п’ятипетлевому наближенні, отримані РГ ряди пересумовуються з використанням техніки Паде-Бореля-Лєруа і конформного перетворення.
Знайдено, що для N = 2 неперервна лінія нерухомих точок добре
відтворюється пересумованими РГ рядами і врахування п’ятипетлевих членів робить лінії нулів обох β функцій ближчими один
до одного. Показано, що для N > 3 п’яти-петлеві внески зсувають
кубічну нерухому точку, отриману в чотири-петлевому наближенні,
до нерухомої точки Ізинґа. Це підтверджує ідею, що існування
кубічної нерухомої точки в двох вимірах під N > 2 є результатом
пертурбативного аналізу. У випадку N = 0 отримані результати є
сумісні з висновком, що критична поведінка, пов’язана з домішками,
контролюється нерухомою точкою Ізинґа
Stability of critical behaviour of weakly disordered systems with respect to the replica symmetry breaking
A field-theoretic description of the critical behaviour of the weakly
disordered systems is given. Directly, for three- and two-dimensional systems a
renormalization analysis of the effective Hamiltonian of model with replica
symmetry breaking (RSB) potentials is carried out in the two-loop
approximation. For case with 1-step RSB the fixed points (FP's) corresponding
to stability of the various types of critical behaviour are identified with the
use of the Pade-Borel summation technique. Analysis of FP's has shown a
stability of the critical behaviour of the weakly disordered systems with
respect to RSB effects and realization of former scenario of disorder influence
on critical behaviour.Comment: 10 pages, RevTeX. Version 3 adds the functions for arbitrary
dimension of syste
Five-loop \sqrt\epsilon-expansions for random Ising model and marginal spin dimensionality for cubic systems
The \sqrt\epsilon-expansions for critical exponents of the weakly-disordered
Ising model are calculated up to the five-loop order and found to possess
coefficients with irregular signs and values. The estimate n_c = 2.855 for the
marginal spin dimensionality of the cubic model is obtained by the Pade-Borel
resummation of corresponding five-loop \epsilon-expansion.Comment: 9 pages, TeX, no figure
Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering
The fixed point that governs the critical behavior of magnets described by
the -vector chiral model under the physical values of () is
shown to be a stable focus both in two and three dimensions. Robust evidence in
favor of this conclusion is obtained within the five-loop and six-loop
renormalization-group analysis in fixed dimension. The spiral-like approach of
the chiral fixed point results in unusual crossover and near-critical regimes
that may imitate varying critical exponents seen in physical and computer
experiments.Comment: 4 pages, 5 figures. Discussion enlarge
Cumulant ratios and their scaling functions for Ising systems in strip geometries
We calculate the fourth-order cumulant ratio (proposed by Binder) for the
two-dimensional Ising model in a strip geometry L x oo. The Density Matrix
Renormalization Group method enables us to consider typical open boundary
conditions up to L=200. Universal scaling functions of the cumulant ratio are
determined for strips with parallel as well as opposing surface fields.Comment: 4 pages, RevTex, one .eps figure; references added, format change
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