The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

AbstractsLet W(x,y) = ax3+ bx4+ f5x5+ f6x6+ (3 ax2)2y+ g5x5y + h3x3y2 + h4x4y2 + n3x3y3+a24x2y4+a05y5+a15xy5+a06y6, and X = , , where the coefficients are non-negative constants, with a > 0, such that X2(x,x2)−Y(x,x2) is a polynomial of x with non-negative coefficients.Examples of the 2 dimension...

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Bibliographic Details
Published in:Journal of statistical physics 2007-05, Vol.127 (3), p.609-627
Main Author: Hattori, Tetsuya
Format: Article
Language:English
Subjects:
Gaskets
Physics
Polynomials
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Summary:AbstractsLet W(x,y) = ax3+ bx4+ f5x5+ f6x6+ (3 ax2)2y+ g5x5y + h3x3y2 + h4x4y2 + n3x3y3+a24x2y4+a05y5+a15xy5+a06y6, and X = , , where the coefficients are non-negative constants, with a > 0, such that X2(x,x2)−Y(x,x2) is a polynomial of x with non-negative coefficients.Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets.We prove that there exists a unique fixed point (xf,yf) of Φ in the invariant set .
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-007-9283-3