Renormalization group approach to critical dynamics in the coupled oscillator problem

1977 ◽  
Vol 49 (2) ◽  
pp. 349-352
Author(s):  
R.J. Abbott ◽  
R.S. Wilson
Keyword(s):  
Renormalization Group ◽  
Critical Dynamics ◽  
Coupled Oscillator ◽  
Group Approach ◽  
Renormalization Group Approach

Field-Theory Description of Nonequilibrium Critical Dynamics for Spin Systems

2012 ◽  
Vol 190 ◽  
pp. 23-26
Author(s):  
Ivan A. Kalashnikov ◽  
Pavel V. Prudnikov
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Order Parameter ◽  
Spin Systems ◽  
Critical Dynamics ◽  
Relaxation Dynamics ◽  
Group Approach ◽  
Fixed Dimension ◽  
Renormalization Group Approach ◽  
Short Time

Renormalization-group approach is applied to investigate the short-time nonequilibriumcritical behavior of pure and diluted spin systems with nonmagnetic point-like impurities.The dissipative relaxation dynamics with non-conserved order parameter is considered. For thefirst time the description of the order parameter growth induced by the initial nonequilibriumstate of system is carried out at fixed dimension d = 3 without use of ε-expansion.

Critical Dynamics of Pitch-Fork Bifurcation in a System Driven by a Fractal Sequence

1998 ◽  
Vol 08 (04) ◽  
pp. 741-746 ◽  
Author(s):  
P. V. Kuptsov
Keyword(s):  
Renormalization Group ◽  
Critical Exponents ◽  
External Perturbation ◽  
Critical Dynamics ◽  
External Influence ◽  
Group Approach ◽  
Strange Nonchaotic Attractor ◽  
Fractal Properties ◽  
Renormalization Group Approach ◽  
Analytical Expressions

We consider the system, exhibiting pitch-fork bifurcation, forced by the external perturbation with fractal properties. Developing a renormalization group approach, we show that the situation is characterized by nonclassical critical exponents. These exponents appear to depend on external influence intensity and we get the analytical expressions for them. Apparently, a new kind of strange nonchaotic attractor arises in the case under consideration.

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