Conformal Invariance, Unitarity and Two Dimensional Critical Exponents

1985 ◽  
pp. 419-449 ◽  
Author(s):  
Daniel Friedan ◽  
Zongan Qiu ◽  
Stephen Shenker
Keyword(s):  
Critical Exponents ◽  
Conformal Invariance ◽  
Two Dimensional

scholarly journals Finding critical exponents for two-dimensional Hamiltonian maps

2010 ◽  
Vol 81 (4) ◽  
Author(s):  
Juliano A. de Oliveira ◽  
R. A. Bizão ◽  
Edson D. Leonel
Keyword(s):  
Critical Exponents ◽  
Two Dimensional

scholarly journals Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Edson D. Leonel
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Scaling Function ◽  
Initial Conditions ◽  
Invariant Tori ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Control Parameters ◽  
Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

Critical exponents for boundary avalanches in two-dimensional Abelian sandpile

1994 ◽  
Vol 27 (16) ◽  
pp. L585-L590 ◽  
Author(s):  
E V Ivashkevich ◽  
D V Ktitarev ◽  
V B Priezzhev
Keyword(s):  
Critical Exponents ◽  
Two Dimensional ◽  
Abelian Sandpile

scholarly journals Universality, frustration, and conformal invariance in two-dimensional random Ising magnets

1999 ◽  
Vol 60 (9) ◽  
pp. 6740-6748 ◽  
Author(s):  
F. D. A. Aarão Reis ◽  
S. L. A. de Queiroz ◽  
Raimundo R. dos Santos
Keyword(s):  
Conformal Invariance ◽  
Two Dimensional ◽  
Ising Magnets
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