Abstract
Using the representation for renormalization group functions in terms of nonsingular integrals, we calculate the dynamical critical exponents in the model of critical dynamics of ferromagnets in the fourth order of the ε-expansion. We calculate the Feynman diagrams using the sector decomposition technique generalized to critical dynamics problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Ts. Adzhemyan and M. V. Kompaniets, “Renormalization group and the ε-expansion: Representation of the β-function and anomalous dimensions by nonsingular integrals,” Theor. Math. Phys., 169, 1450–1459 (2011).
L. Ts. Adzhemyan, M. V. Kompaniets, S. V. Novikov, and V. K. Sazonov, “Representation of the β-function and anomalous dimensions by nonsingular integrals: Proof of the main relation,” Theor. Math. Phys., 175, 717–726 (2013).
L. Ts. Adzhemyan, S. E. Vorobyeva, and M. V. Kompaniets, “Representation of the β-function and anomalous dimensions by nonsingular integrals in models of critical dynamics,” Theor. Math. Phys., 185, 1361–1369 (2015).
P. C. Hohenberg and B. I. Halperin, “Theory of dynamic critical phenomena,” Rev. Modern Phys., 49, 435–479 (1977).
T. Binoth and G. Heinrich, “An automatized algorithm to compute infrared divergent multi-loop integrals,” Nucl. Phys. B, 585, 741–759 (2000).
A. N. Vasil’ev, Quantum Field Renormalization Group in Critical Behavior Theory and Stochastic Dynamics [in Russian], Petersburg Inst. Nucl. Phys., St. Petersburg (1998) English transl.: The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics, Chapman and Hall/CRC, Boca Raton, Fla. (2004).
O. I. Zav’yalov, Renormalized Feynman Diagrams [in Russian], Nauka, Moscow (1979) English transl., Kluwer Academic, Dordrecht (1988).
L. Ts. Adzhemyan, Yu. V. Kirienko, and M. V. Kompaniets, “Critical exponent η in 2D O(N)-symmetric ϕ4-model up to 6 loops,” arXiv:1602.02324v1 [cond-mat.stat-mech] (2016).
L. Ts. Adzhemyan and M. V. Kompaniets, “Five-loop numerical evaluation of critical exponents of the ϕ4 theory,” J. Phys.: Conf. Ser., 523, 012049 (2014).
B. I. Halperin, P. C. Hohenberg, and S.-K. Ma, “Calculation of dynamic critical properties using Wilson’s expansion methods,” Phys. Rev. Lett., 29, 1548–1551 (1972).
N. V. Antonov and A. N. Vasil’ev, “Critical dynamics as a field theory,” Theor. Math. Phys., 60, 671–679 (1984).
L. Ts. Adzhemyan, S. V. Novikov, and L. Sladkoff, “Calculation of the dynamical exponent of model A of critical dynamics in the order ε4 [in Russian],” Vestn. S. Peterburg. Un-ta. Ser. 4: Fizika, Khimiya, No. 4, 109–112 (2008).
E. R. Speer, “Mass singularities of generic Feynman amplitudes,” Ann. Inst. Henri Poincaré Sect. A, n.s., 26, 87–105 (1977).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Adzhemyan, L.T., Vorob’eva, S.E., Ivanova, E.V. et al. Representation of Renormalization Group Functions By Nonsingular Integrals in a Model of the Critical Dynamics of Ferromagnets: The Fourth Order of The ε-Expansion. Theor Math Phys 195, 584–594 (2018). https://doi.org/10.1134/S0040577918040104
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577918040104