arXiv subjects

V. A. Ul'kov

Publications and source records attributed to V. A. Ul'kov.

4 recordsLinked to original sources

arXiv1999

Universal critical coupling constants for the three-dimensional n-vector model from field theory

The field-theoretical renormalization group approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g_6 and g_8 for the O(n)-symmetric model. The RG series for g_6 and g_8 are calculated in the four-loop and three-loop approximations respectively and then resummed by means of the Pade-Borel-Leroy technique. Under the optimal value of the shift parameter b providing the fastest convergence of the iteration procedure numerical estimates for the universal critical values g_6^*(n) are obtained for n = 1, 2, 3,...40 with the accuracy no worse than 0.3%. The RG expansion for g_8 demonstrates stronger divergence and results in considerably cruder numerical estimates. They are found to be consistent with the values of g_8^* deduced from the exact RG equations and, for n > 8, with those given by a constrained analysis of corresponding ε-expansion.

hep-th↗

arXiv1998

Universal effective action for O(n)-symmetric λϕ^4 model from renormalization group

The RG expansions for renormalized coupling constants g_6 and g_8 of the 3D n-vector model are calculated in the 4-loop and 3-loop approximations respectively. Resummation of the RG series for g_6 by the Pade-Borel-Leroy technique results in the estimates for its universal critical values g_6^*(n) which are argued to deviate from the exact numbers by less than 0.3%. The RG expansion for g_8 demonstrates stronger divergence being much less suitable for getting reliable numerical estimates.

hep-th↗

arXiv1998

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.

cond-mat.stat-mech↗

arXiv1998

On free energy of three-dimensional Ising model at criticality

Higher-order vertices at zero external momenta for the scalar field theory describing the critical behaviour of the Ising model are studied within the field-theoretical renormalization group (RG) approach in three dimensions. Dimensionless six-point g_6 and eight-point g_8 effective coupling constants are calculated in the three-loop approximation. Their numerical values, universal at criticality, are estimated by means of the Pade and Pade-Borel summation of the RG expansions found and by putting the renormalized quartic coupling constant equal to its universal fixed-point value known from six-loop RG calculations. The values of g_6^* obtained are compared with their analogs resulting from the ε-expansion, Monte Carlo simulations, the Wegner--Houghton equations and the linked cluster expansion series. The field-theoretical estimates for g_6^* are shown to be in a good agreement with each other, differing considerably from the values given by other methods.

cond-mat.stat-mech↗