A new approach to summation of divergent field-theoretical series is suggested. It is based on th... more A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is tested on functions expanded in their asymptotic power series and applied to estimating the ground state energy of simple quantum mechanical problems including anisotropic oscillators and caclulating the critical exponents for certain comformal field models. It can be expected that the new approach to summation may be used to obtaining numerical estimates for important physical quantities represented by divergent series in two- and three-dimensional field models.
The critical thermodynamics of an MN-component field model with cubic anisotropy relevant to the ... more The critical thermodynamics of an MN-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop [iopmath latex="$\varepsilon$"] [/iopmath] expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases [iopmath latex="$M=2$"] M = 2 [/iopmath] , [iopmath latex="$N=2$"] N = 2 [/iopmath] and [iopmath latex="$M=2$"] M = 2 [/iopmath] , [iopmath latex="$N=3$"] N = 3 [/iopmath] shows that the model has an anisotropic stable fixed point with new critical exponents. The critical dimensionality of the order parameter is proved to be equal to [iopmath latex="$N_{\rm c}^{\rm C}=1.445(20)$"] NcC = 1.445(20) [/iopmath] , that is exactly half its counterpart in the real hypercubic model.
The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferrom... more The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferromagnets with 2N-component (N>1) real order parameters as well as the structural transition in NbO2 crystal is studied within the field-theoretical renormalization-group (RG) approach in three and (4-ε)-dimensions. Perturbative expansions for RG functions are calculated up to three-loop order and resummed, in 3D, by means of the
A new approach to summation of divergent field-theoretical series is suggested. It is based on th... more A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is tested on functions expanded in their asymptotic power series and applied to estimating the ground state energy of simple quantum mechanical problems including anisotropic oscillators and caclulating the critical exponents for certain comformal field models. It can be expected that the new approach to summation may be used to obtaining numerical estimates for important physical quantities represented by divergent series in two- and three-dimensional field models.
The critical thermodynamics of an MN-component field model with cubic anisotropy relevant to the ... more The critical thermodynamics of an MN-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop [iopmath latex="$\varepsilon$"] [/iopmath] expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases [iopmath latex="$M=2$"] M = 2 [/iopmath] , [iopmath latex="$N=2$"] N = 2 [/iopmath] and [iopmath latex="$M=2$"] M = 2 [/iopmath] , [iopmath latex="$N=3$"] N = 3 [/iopmath] shows that the model has an anisotropic stable fixed point with new critical exponents. The critical dimensionality of the order parameter is proved to be equal to [iopmath latex="$N_{\rm c}^{\rm C}=1.445(20)$"] NcC = 1.445(20) [/iopmath] , that is exactly half its counterpart in the real hypercubic model.
The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferrom... more The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferromagnets with 2N-component (N>1) real order parameters as well as the structural transition in NbO2 crystal is studied within the field-theoretical renormalization-group (RG) approach in three and (4-ε)-dimensions. Perturbative expansions for RG functions are calculated up to three-loop order and resummed, in 3D, by means of the
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Papers by Andrey Mudrov