Modified critical behavior in the $\varphi^4(O_n)$ model

In the standard $\varphi^4(O_n)$ model, a critical regime in which the coupling constant $g$ of the $\varphi^4$ decreases as a certain given power $\tau^\alpha$ as $\tau\equiv T-T_c\to0$ is considered. From the point of view of physics, such a formulation of the problem corresponds to a certain class of trajectories of approach to the triple point in the two-dimensional plane of the physical parameters of the system. It is shown that in such a “modified critical regime” all the critical dimensions can be expressed in terms of the specified value of the exponent $\alpha$ and the ordinary critical dimensions of the $\varphi^4$ model known in the form of $4-\varepsilon$ expansions.