Searcharxiv⌕ Search

arXiv subjects

I. M. Suslov

Publications and source records attributed to I. M. Suslov.

67 records · Page 4Linked to original sources
arXiv2005

High-Order Corrections to the Lipatov Asymptotics in the ϕ^4 Theory

High orders in perturbation theory can be calculated by the Lipatov method. For most field theories, the Lipatov asymptotics has the functional form c a^N Γ(N+b) (N is the order of perturbation theory); relative corrections to this asymptotics have the form of a power series in 1/N. The coefficients of high order terms of this series can be calculated using a procedure analogous to the Lipatov approach and are determined by the second instanton in the considered field theory. These coefficients are calculated quantitatively for the n-component ϕ^4 theory under the assumption that the second instanton is (i) a combination of two elementary instantons and (ii) a spherically asymmetric localized function. The technique of two-instanton calculations is developed, as well as the method for integrating over rotations of an asymmetric instanton in the coordinate state.

hep-ph↗
arXiv2001

Summing Divergent Perturbative Series in a Strong Coupling Limit. The Gell-Mann - Low Function of the ϕ^4 Theory

An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for estimating errors is developed, and an optimization procedure is described. Application of the algorithm to the $ϕ^4$ theory gives a behavior $β(g)\approx 7.4 g^{0.96}$ at large $g$ for its Gell-Mann -- Low function. The fact that the exponent is close to unity can be interpreted as a manifestation of the logarithmic branching of the type $β(g)\sim g (\ln g)^{-γ}$ (with $γ\approx 0.14$), which is confirmed by independent evidence. In any case, the $ϕ^4$ theory is internally consistent. The procedure of summing perturbartive series with arbitrary values of expansion parameter is discussed.

hep-ph↗
arXiv2000

Scaling near the upper critical dimensionality in the localization theory

The phenomenon of upper critical dimensionality d_c2 has been studied from the viewpoint of the scaling concepts. The Thouless number g(L) is not the only essential variable in scale transformations, because there is the second parameter connected with the off-diagonal disorder. The investigation of the resulting two-parameter scaling has revealed two scenarios, and the switching from one to another scenario determines the upper critical dimensionality. The first scenario corresponds to the conventional one-parameter scaling and is characterized by the parameter g(L) invariant under scale transformations when the system is at the critical point. In the second scenario, the Thouless number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation of the Wegner relation s=ν(d-2) between the critical exponents for conductivity (s) and for localization radius (ν), which takes the form s=ν(d_c2-2). The resulting formulas for g(L) are in agreement with the symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous version of Mott's argument concerning localization due topological disorder has been proposed.

cond-mat.dis-nn↗
arXiv2000

Structure of High Order Corrections to Lipatov's Asymptotics

High orders of perturbation theory can be calculated by the Lipatov method, whereby they are determined by saddle-point configurations (instantons) of the corresponding functional integrals. For most field theories, the Lipatov asymptotics has the functional form c a^N Γ(N+b) (N is the order of perturbation theory), and the relative corrections to it have a form of a series in powers of 1/N. It is shown that this series diverges factorially and its high-order coefficients can be calculated using a procedure similar to Lipatov's one. The K-th expansion coefficient has the form const(\ln(S1/S0))^{-K}Γ(K+(r1-r0)/2), where S0 and S1 are the values of the action for the first and the second instanton of the field theory under consideration, while r0 and r1 are the corresponding numbers of zero modes. The instantons satisfy the same equation as in the Lipatov method and are assumed to be renumbered in order of increasing of their action. This result has the universal character and is valid in any field theory for which the Lipatov asymptotic form is as specified above.

hep-ph↗
arXiv2000

Gell-Mann - Low Function in the Phi^4 Theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the Φ^4 theory, the algorithm yields the β(g)\propto g^αbehavior with α\approx 1 at large g for the Gell-Mann - Low function.

hep-ph↗
arXiv1999

Development of (4-epsilon)-dimensional theory for the density of states near the Anderson transition

The density of states for the Schroedinger equation with a Gaussian random potential is determined by the functional integral corresponding to the phi^4 theory with a `wrong' sign of the interaction constant. The special role of the dimension d=4 for such a problem can be seen from different viewpoints but is fundamentally determined by the renormalizability of the theory. The construction of an epsilon-expansion in direct analogy with the phase-transition theory gives rise to the problem of a `spurious' pole. To solve this problem, a proper treatment of the factorial divergency of the perturbation series is necessary. Simplifications arising in high dimensions can be used for the development of a (4-epsilon)-dimensional theory, but this requires successive consideration of four types of theories: a nonrenormalizable theory for d>4, nonrenormalizable and renormalizable theories in the logarithmic situation (d=4), and a super-renormalizable theory for d<4. An approximation is found for each type of theory giving asymptotically exact results. The qualitative effect is the same in all four cases and consists in a shifting of the phase transition point in the complex plane. This results in the elimination of the `spurious' pole and in regularity of the density of states for all energies. A discussion is given of the calculation of high orders of perturbation theory and a perspective of the epsilon-expansion for the problem of conductivity near the Anderson transition.

cond-mat.dis-nn↗
arXiv1999

Why have no manifestations of the excitonic mechanism have been detected in Ginzburg sandwiches?

The Ginzburg sandwich is a superconducting film coated with a dielectric layer containing Bose-type exitations, i.e. exitons. Using spatially inhomogeneous Eliashberg equations in the local interaction limit, an exact result for the superconducting transition temperature of the Ginzburg sandwich has been obtained in the first order in a/L (where a is interatomic distance and L is the film thickness). The result has been found to be independent of the exiton frequency. The exitonic mechanism appears only in the second order in a/L since both partners of the Cooper pair should enter a layer of thickness \sim a in order to interact through exchange of exitons. Numerical estimates indicate that manifestations of the exitonic mechanism are practically undetectable in systems with L>>a. Calculations for a narrow-gap and wide-gap dielectric have been performed and compared to experimental data.

cond-mat.supr-con↗
arXiv1999

Upper critical dimension in the scaling theory of localization

It is argued that the Thouless number g(L) is not the only parameter relevant in scale transformations, and that the second parameter connected with off-diagonal disorder should be introduced. A two-parameter scaling theory is suggested that explains a phenomenon of the upper critical dimension from the viewpoint of scaling ideas.

cond-mat.dis-nn↗
arXiv1999

Density of States near the Anderson Transition in a Space of Dimensionality d=4-epsilon

Asymptotically exact results are obtained for the average Green function and the density of states in a Gaussian random potential for the space dimensionality d=4-epsilon over the entire energy range, including the vicinity of the mobility edge. For N\sim 1 (N is an order of the perturbation theory) only the parquet terms corresponding to the highest powers of 1/epsilon are retained. For large N all powers of 1/epsilon are taken into account with their coefficients calculated in the leading asymptotics in N. This calculation is performed by combining the condition of renormalizability of the theory with the Lipatov asymptotics.

cond-mat.dis-nn↗
arXiv1999

Density of States near the Anderson Transition in a Four-dimensional Space. Renormalizable Models

Asymptotically exact results are obtained for the average Green function and density of states of a disordered system for a renormalizable class of models (as opposed to the lattice models examined previously [Zh. Eksp. Teor. Fiz. 106 (1994) 560-584]). For N\sim 1 (where N is an order of the perturbation theory), only the parquet terms corresponding to the highest powers of large logarithms are retained. For large N, this approximation is inadequate because of the fast growth with N of the coefficients for the lower powers of the logarithms. The latter coefficients are calculated in the leading order in N from the Callan-Symanzik equation with results of the Lipatov method using as boundary conditions. For calculating the self-energy at finite momentum, a modification of the parquet approximation is used, that allows the calculations to be done in an arbitrary finite logarithmic approximation but in the leading order in N. It is shown that the phase transition point shifts in the complex plane, thereby insuring regularity of the density of states for all energies. The "spurious" pole is avoided in such a way that effective interaction remains logarithmically weak.

cond-mat.dis-nn↗
arXiv1997

Density of States of an Electron in a Gaussian Random Potential for (4-epsilon)-dimensional Space

The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are taken into account for N \sim 1 (N is an order of perturbation theory) while all powers of 1/epsilon are essential for N>>1 with calculation of the expansion coefficients in the leading order in N.

cond-mat.dis-nn↗