Birth of a new class of period-doubling scaling behavior as a result of bifurcation in the renormalization equation

作者：Kuznetsov S P^*; Mailybaev A A; Sataev I R

来源：Journal of Statistical Physics, 2008, 130(3): 599-616.

DOI：10.1007/s10955-007-9442-6

It is found that a fixed point of the renormalization group equation corresponding to a system of a unimodal map with extremum of power kappa and a map summarizing values of a function of the dynamical variable of the first subsystem, undergoes a bifurcation in the course of increase of kappa. It occurs at kappa(c)=1.984396 and results in a birth of the period-2 stationary solution of the RG equation. At kappa=2 this period-2 solution corresponds to the universal period-doubling behavior discovered earlier and denoted as the C-type criticality (Kuznetsov and Sataev in Phys. Lett. A 162:236-242, 1992). By combination of analytical methods and numerical computations we obtain and analyze an asymptotic expansion of the period-2 solution in powers of Delta kappa=kappa- kappa(c). The developed approach resembles the epsilon-expansion in the phase transition theory, in which a "trivial" stationary point of the RG transformation undergoes a bifurcation that gives rise to a new fixed point responsible for the critical behavior with nontrivial critical indices.

• 出版日期2008-2