Speaker
Description
In this talk we understand by "dimensional transmutation" a situation when, in a certain field theoretic model, a certain canonically dimensionless parameter (like a coupling constant) acquires a nontrival critical dimension in the infrared asymptotic range of scales (long times, large distances). This situation is not unfrequent and was encountered in stochastic magnetic hydrodynamics, turbulent advection of chemically active agent, kinetic roughening of growing surfaces and so on.
Another kind of dimensional transmutation is the situation when a weakly anisotropic model becomes strongly anisotropic in a certain asymptotic regime, corresponding to a certain exceptional fixed point of the renormalization group equation. It is illustrated by the example of strongly anisotropic Hwa-Kardar model of self-organized criticality ("running sandpile" ) coupled with an isotropic environment, described by a certain statistical velocity ensemble for an incompressible fluid.
The original stochastic Hwa-Kardar equation allows for independent scaling of spatial coordinates, the coordinate along the preferred dimension and the coordinates in the orthogonal subspace. This strongly anisotropic behaviour is ruined once the isotropic velocity ensemble is added. However, it is restored in a special asymptotic regime in which the interaction with the environment becomes irrelevant. The mechanism behind this restoration is also based on a specific type of dimensional transmutation.
N.V. A., N.M. Gulitskiy, P. I. Kakin, M.N. Semeikin "Dimensional transmutation and nonconventional scaling behaviour in a model of self-organized criticality" Int. J. Mod. Phys. A37, 2240022 (2022)
N. V. A., N.M. Gulitskiy, P. I.Kakin, G.E.Kochnev "Effects of turbulent environment on self-organized critical behaviour: Isotropy vs anisotropy" Universe 6, 145 (2020)
