11 research outputs found
Field-theoretic analysis of directed percolation: Three-loop approximation
The directed bond percolation is a paradigmatic model in nonequilibrium
statistical physics. It captures essential physical information on the nature
of continuous phase transition between active and absorbing states. In this
paper, we study this model by means of the field-theoretic formulation with a
subsequent renormalization group analysis. We calculate all critical exponents
needed for the quantitative description of the corresponding universality class
to the third order in perturbation theory.
Using dimensional regularization with minimal subtraction scheme, we carry
out perturbative calculations in a formally small parameter ,
where
is a deviation from the upper critical dimension . We use a nontrivial
combination of analytical and numerical tools in order to determine ultraviolet
divergent parts of Feynman diagrams
Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation
The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ε = 4 − d
Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
Statistical model of strongly anisotropic fully developed turbulence of the
weakly compressible fluid is considered by means of the field theoretic
renormalization group. The corrections due to compressibility to the infrared
form of the kinetic energy spectrum have been calculated in the leading order
in Mach number expansion. Furthermore, in this approximation the validity of
the Kolmogorov hypothesis on the independence of dissipation length of velocity
correlation functions in the inertial range has been proved.Comment: REVTEX file with EPS figure
Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
Field theoretical renormalization group methods are applied to a simple model
of a passive scalar quantity advected by the Gaussian non-solenoidal
(``compressible'') velocity field with the covariance . Convective range anomalous scaling for the structure
functions and various pair correlators is established, and the corresponding
anomalous exponents are calculated to the order of the
expansion. These exponents are non-universal, as a result of the degeneracy of
the RG fixed point. In contrast to the case of a purely solenoidal velocity
field (Obukhov--Kraichnan model), the correlation functions in the case at hand
exhibit nontrivial dependence on both the IR and UV characteristic scales, and
the anomalous scaling appears already at the level of the pair correlator. The
powers of the scalar field without derivatives, whose critical dimensions
determine the anomalous exponents, exhibit multifractal behaviour. The exact
solution for the pair correlator is obtained; it is in agreement with the
result obtained within the expansion. The anomalous exponents for
passively advected magnetic fields are also presented in the first order of the
expansion.Comment: 31 pages, REVTEX file. More detailed discussion of the
one-dimensional case and comparison to the previous paper [20] are given;
references updated. Results and formulas unchange
Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation
The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ε = 4 − d
Renormalization Approach to the Gribov Process: Numerical Evaluation of Critical Exponents in Two Subtraction Schemes
We study universal quantities characterizing the second order phase transition in the Gribov process. To this end, we use numerical methods for the calculation of the renormalization group functions up to two-loop order in perturbation theory in the famous ε-expansion. Within this procedure the anomalous dimensions are evaluated using two different subtraction schemes: the minimal subtraction scheme and the null-momentum scheme. Numerical calculation of integrals was done on the HybriLIT cluster using the Vegas algorithm from the CUBA library. The comparison with existing analytic calculations shows that the minimal subtraction scheme yields more precise results
Renormalization Approach to the Gribov Process: Numerical Evaluation of Critical Exponents in Two Subtraction Schemes
We study universal quantities characterizing the second order phase transition in the Gribov process. To this end, we use numerical methods for the calculation of the renormalization group functions up to two-loop order in perturbation theory in the famous ε-expansion. Within this procedure the anomalous dimensions are evaluated using two different subtraction schemes: the minimal subtraction scheme and the null-momentum scheme. Numerical calculation of integrals was done on the HybriLIT cluster using the Vegas algorithm from the CUBA library. The comparison with existing analytic calculations shows that the minimal subtraction scheme yields more precise results