Speaker
Description
Tricritical behavior in systems with an $n$-component order parameter $\varphi = \{\varphi_a, a = 1, \ldots, n\}$ is described by the action $S(\varphi) = \frac{1}{2}\partial_i\varphi_a\partial_i\varphi_a + \frac{\tau}{2} \varphi_a\varphi_a + \frac{\lambda}{4!} (\varphi_a\varphi_a)^2 + \frac{g}{6!} (\varphi_a\varphi_a)^3$, where the coefficients $\tau$, $\lambda$ and $g$ are parameters of the model [1].
Six-loop calculation of the renormalization group functions in the model was carried out in $d = 3 - \varepsilon$ dimensions using the dimensional regularization. The model was renormalized within the minimal subtraction scheme (MS) [1]. All diagrams, except seven diagrams, were calculated with G-functions [2]. For the remaining seven six-loop diagrams, the G-function approach allowed to reduce them to two-loop diagrams, which were computed numerically using the Sector Decomposition method [3]. The results obtained differ from those previously known [4].
The work is supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075–15–2022–287).
[1] A.N. Vasil’ev, Quantum field renormalization group in critical behavior theory and stochastic dynamics. Chapman and Hall/CRC (2004).
[2] K.G. Chetyrkin and F.V. Tkachov, New approach to evaluation of multiloop Feynman integrals: The Gegenbauer polynomial x-space technique. Nucl. Phys. B, 174, 345 -- 377 (1980).
[3] G. Heinrich, Sector Decomposition. Int. J. Mod. Phys. A, 23, 1457 -- 1486 (2008).
[4] J.S. Hager, Six-loop renormalization group functions of $O(n)$-symmetric $\phi^6$-theory and $\epsilon$-expansions of tricritical exponents up to $\epsilon^3$. J. Phys. A: Math. Gen., 35, 2703 -- 2711 (2002).
