Tricritical Exponents and Scaling Fields

1972 ◽  
Vol 29 (6) ◽  
pp. 349-352 ◽  
Author(s):  
Eberhard K. Riedel ◽  
Franz J. Wegner
Keyword(s):  
Scaling Fields

Multisingularity and scaling in partial differential approximants. I

1988 ◽  
Vol 419 (1857) ◽  
pp. 181-203 ◽  
Keyword(s):  
Scaling Function ◽  
Linear Partial Differential Equation ◽  
Linear Combinations ◽  
Partial Differential ◽  
Polynomial Coefficients ◽  
Explicit Formulae ◽  
Expansion Coefficients ◽  
Scaling Fields ◽  
The Scaling Function ◽  
Asymptotic Scaling

A partial differential approximant (or PDA), F ( x, y ) approximates a function f ( x, y ), specified by its truncated power series, in terms of a solution of a defining linear partial differential equation with polynomial coefficients. The intrinsic multisingularities of a PDA, which may approximate corresponding singularities of f ( x, y ), are analysed formally and shown to obey, in general, asymptotic scaling (as familiar in the theory of critical phenomena), i. e. F ( x, y ) ≈ C | x͠ | - γ Z ( y͠ /| x͠ | ϕ ) + B , where x͠ and y͠ are linear combinations of the deviations, ( x - x c ) and ( y - y c ), from the multisingular point ( x c , y c ). Explicit formulae, suitable for numerical computation, are derived for the characteristic exponents, γ and ϕ , for the scaling function Z ( • ), for its expansion coefficients and for the related coefficients C and B , in the case when the crossover exponent, ϕ , lies in the interval (½, 2). (Part II extends these results to general values of ϕ , which requires the introduction of the nonlinear scaling fields associated with the PDA.)

Nonlinear scaling fields and corrections to scaling near criticality

1983 ◽  
Vol 27 (7) ◽  
pp. 4394-4400 ◽  
Author(s):  
Amnon Aharony ◽  
Michael E. Fisher
Keyword(s):  
Corrections To Scaling ◽  
Scaling Fields

Expectation values of scaling fields in Z N Ising models

2008 ◽  
Vol 154 (3) ◽  
pp. 473-494 ◽  
Author(s):  
V. A. Fateev ◽  
Y. P. Pugai
Keyword(s):  
Ising Models ◽  
Expectation Values ◽  
Scaling Fields

scholarly journals Order Parameter and Scaling Fields in Self-Organized Criticality

1997 ◽  
Vol 78 (25) ◽  
pp. 4793-4796 ◽  
Author(s):  
Alessandro Vespignani ◽  
Stefano Zapperi
Keyword(s):  
Order Parameter ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Scaling Fields

Scaling fields and universality of the liquid-gas critical point

1992 ◽  
Vol 68 (2) ◽  
pp. 193-196 ◽  
Author(s):  
A. D. Bruce ◽  
N. B. Wilding
Keyword(s):  
Critical Point ◽  
Scaling Fields
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