arXiv subjects

Konstantin Varnashev

Publications and source records attributed to Konstantin Varnashev.

8 recordsLinked to original sources

arXiv2001

Critical behavior of certain antiferromagnets with complicated ordering: Four-loop $\ve$-expansion analysis

The critical behavior of a complex N-component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in $(4-\ve)$ dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N=2 and N=3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality $N_c=1.445(20)$ obtained from six loops via the exact relation $N_c={1/2} n_c$ established for the complex and real hypercubic models.

cond-mat.stat-mech↗

arXiv2001

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Within the four-loop $\ve$ expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality $N_c^C=1.445(20)$ obtained from six loops via the exact relation $N_c^C={1/2} N_c^R$ established for the real and complex hypercubic models.

cond-mat.stat-mech↗

arXiv2001

Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop εexpansion

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 $\ve$ expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases M=2, N=2 and M=2, N=3 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 $N_c^C=1.445(20)$, that is exactly half its counterpart in the real hypercubic model.

cond-mat.stat-mech↗

arXiv2000

The stability of a cubic fixed point in three dimensions from the renormalization group

The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the $\bt$-functions are calculated for arbitrary $N$. The critical dimensionality $N_c=2.89 \pm 0.02$ and the stability matrix eigenvalues estimates obtained on the basis of the generalized Pad$\acute{\rm e}$-Borel-Leroy resummation technique are shown to be in a good agreement with those found recently by exploiting the five-loop $\ve$-expansions.

cond-mat.stat-mech↗

arXiv2000

Stability of a cubic fixed point in three dimensions. Critical exponents for generic N

The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D) within an assumption of isotropic exchange. Perturbative expansions for RG functions are calculated for arbitrary $N$ up to the four-loop order and resummed by means of the generalized Pad$\acute{\rm e}$-Borel-Leroy technique. Coordinates and stability matrix eigenvalues for the cubic fixed point are found under the optimal value of the transformation parameter. Critical dimensionality of the model is proved to be equal to $N_c=2.89 \pm 0.02$ that agrees well with the estimate obtained on the basis of the five-loop $\ve$-expansion [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B342, 284 (1995)] resummed by the above method. As a consequence, the cubic fixed point should be stable in 3D for $N\ge3$, and the critical exponents controlling phase transitions in three-dimensional magnets should belong to the cubic universality class. The critical behavior of the random Ising model being the nontrivial particular case of the cubic model when N=0 is also investigated. For all physical quantities of interest the most accurate numerical estimates with their error bounds are obtained. The results achieved in the work are discussed along with the predictions given by other theoretical approaches and experimental data.

cond-mat.stat-mech↗

arXiv1998

New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop εexpansions

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 exact asymptotic parameters to be known. The method is tested on functions expanded in their asymptotic power series. It is applied to estimating the critical exponent values for an N-vector field model, describing magnetic and structural phase transitions in cubic and tetragonal crystals, from five-loop εexpansions.

cond-mat.stat-mech↗

arXiv1998

On stability of the three-dimensional fixed point in a model with three coupling constants from the $ε$ expansion: Three-loop results

The structure of the renormalization-group flows in a model with three quartic coupling constants is studied within the $ε$-expansion method up to three-loop order. Twofold degeneracy of the eigenvalue exponents for the three-dimensionally stable fixed point is observed and the possibility for powers in $\sqrtε$ to appear in the series is investigated. Reliability and effectiveness of the $ε$-expansion method for the given model is discussed.

cond-mat.stat-mech↗

arXiv1997

Three-loop renormalization group analysis of a complex model with stable fixed point: Critical exponents up to $ε^3$ and $ε^4$

The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach in $D=4-2ε$ dimensions. Perturbation expansions for RG functions are calculated using dimensional regularization and the minimal subtraction (MS) scheme. It is shown that for $N\ge 2$ the model does possess a stable fixed point in three dimensional space of coupling constants, in accordance with predictions made earlier on the base of the lower-order approximations. Numerical estimate for critical (marginal) value of the order parameter dimensionality $N_c$ is given using Padé-Borel summation of the corresponding $ε$--expansion series obtained. It is observed that two-fold degeneracy of the eigenvalue exponents in the one-loop approximation for the unique stable fixed point leads to the substantial decrease of the accuracy expected within three loops and may cause powers of $\sqrtε$ to appear in the expansions. The critical exponents $γ$ and $η$ are calculated for all fixed points up to $ε^3$ and $ε^4$, respectively, and processed by the Borel summation method modified with a conformal mapping. For the unique stable fixed point the magnetic susceptibility exponent $γ$ for N=2 is found to differ in third order in $ε$ from that of an O(4)--symmetric point. Qualitative comparison of the results given by $ε$--expansion, three-dimensional RG analysis, non-perturbative RG arguments, and experimental data is performed.

cond-mat↗