Field theoretic renormalization group in a model of random walk on a random surface

N. V. Antonov^ab, P. I. Kakin^ab, A. Yu. Luchin<sup>a

a</sup> St.Petersburg State University, 7/9 Universitetskaya Nab., St.Petersburg 199034, Russia
^b N. N. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia

Abstract: Using the problem of random walk on a random rough surface, we show how neglecting a formally infrared irrelevant (in the sense of Wilson) term in the corresponding action functional makes the regime of non-trivial infrared asymptotic behaviour undetectable. By taking that term into account and employing a nonconventional renormalization scheme in the real $d$-dimensional space, we establish the “weak” scaling behaviour of the Green's functions with two coexisting different expressions for the critical dimension of time/frequency.

Key words and phrases: random walks, kinetic roughening, critical dynamics, renormalization group, weak scaling.

UDC: 519.216, 539.1.01

Received: 17.11.2025

Language: English