scholarly journals Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior

1971 ◽  
Vol 4 (9) ◽  
pp. 3184-3205 ◽  
Author(s):  
Kenneth G. Wilson
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Critical Phenomena ◽  
Critical Behavior ◽  
Cell Analysis ◽  
Space Cell

Renormalization-group approach to antiferromagnetic critical behavior

1974 ◽  
Vol 10 (9) ◽  
pp. 3906-3912 ◽  
Author(s):  
V. A. Alessandrini ◽  
H. J. de Vega ◽  
F. Schaposnik
Keyword(s):  
Renormalization Group ◽  
Critical Behavior ◽  
Group Approach ◽  
Renormalization Group Approach

Renormalization Group

2020 ◽  
pp. 289-318
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Critical Phenomena ◽  
Degrees Of Freedom ◽  
Gaussian Model ◽  
Coupling Constants ◽  
Quantum Field ◽  
Important Notion ◽  
Effective Hamiltonians

Chapter 8 introduces the key ideas of the renormalization group, including how they provide a theoretical scheme and a proper language to face critical phenomena. It covers the scaling transformations of a system and their implementations in the space of the coupling constants and reducing the degrees of freedom. From this analysis, the reader is led to the important notion of relevant, irrelevant and marginal operators and then to the universality of the critical phenomena. Furthermore, the chapter also covers (as regards the RG) transformation laws, effective Hamiltonians, the Gaussian model, the Ising model, operators of quantum field theory, universal ratios, critical exponents and β‎-functions.

scholarly journals On The Critical Phenomena in The Dynamics of Asteroids

1999 ◽  
Vol 172 ◽  
pp. 383-386
Author(s):  
Ivan I. Shevchenko
Keyword(s):  
Phase Space ◽  
Critical Phenomena ◽  
Power Law ◽  
Anomalous Transport ◽  
Selection Effects ◽  
Recurrence Times ◽  
Statistical Selection ◽  
Power Law Decay ◽  
Statistical Effects

AbstractTwo statistical effects in the long-term chaotic asteroidal dynamics are considered, namely the power-law character of the dependence of recurrence times on local Lyapunov times and the power-law decay in the tails of the recurrence distributions. The dependences in both cases are shaped by effects of anomalous transport, due to the presence of the chaos border in phase space, and by statistical selection effects.

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