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Six-loop renormalization group analysis of the model.

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Title: Six-loop renormalization group analysis of the model.
Authors: Adzhemyan, L. Ts.1,2 (AUTHOR), Kompaniets, M. V.1,2 (AUTHOR) mkompan@gmail.com, Trenogin, A. V.1,2 (AUTHOR)
Source: Theoretical & Mathematical Physics. Jun2026, Vol. 227 Issue 3, p925-936. 12p.
Subjects: Renormalization group, Critical exponents, Conformal field theory, Asymptotic expansions
Abstract: We investigate the model using the renormalization group method and the expansion. This model is used in a situation where the coefficients , , and the coefficient of the term depend on two parameters and , and there is a point () at which and are zero. This point is called the tricritical point. The description of the system depends on the trajectory leading to the tricritical point on the plane (). Along trajectories where approaches zero sufficiently fast, the asymptotic description is defined by the interaction and thus the term can be considered as a composite operator. In this case, the logarithmic dimension is , and the expansion is carried out in the dimension. The main exponents of the tricritical model have been calculated in the third order of the expansion. Taking into account the interaction, we were able to calculate the parameter that determines the required decay rate of to implement the tricritical behavior. The tricritical dimensions of the composite operators for have been computed. The resulting values are compared to those known from a conformal field theory and nonperturbative renormalization group. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We investigate the model using the renormalization group method and the expansion. This model is used in a situation where the coefficients , , and the coefficient of the term depend on two parameters and , and there is a point () at which and are zero. This point is called the tricritical point. The description of the system depends on the trajectory leading to the tricritical point on the plane (). Along trajectories where approaches zero sufficiently fast, the asymptotic description is defined by the interaction and thus the term can be considered as a composite operator. In this case, the logarithmic dimension is , and the expansion is carried out in the dimension. The main exponents of the tricritical model have been calculated in the third order of the expansion. Taking into account the interaction, we were able to calculate the parameter that determines the required decay rate of to implement the tricritical behavior. The tricritical dimensions of the composite operators for have been computed. The resulting values are compared to those known from a conformal field theory and nonperturbative renormalization group. [ABSTRACT FROM AUTHOR]
ISSN:00405779
DOI:10.1134/S0040577926060012