Strict inequalities for some critical exponents in two-dimensional perclation
For 2D percolation the authors slightly improve a result of Chayes and Chayes to the effect that the critical exponent ..beta.. for the percolation probability is strictly less than 1. The same argument is applied to prove that if Theta(phi):=/(x,y): x = r cos theta, y = r sin theta for some r greater than or equal to 0, or theta less than or equal to phi/ and ..beta.. (phi): = lim/sub p downward arrow p/sub c//(log(p-p/sub c/))/sup -1/ log P/sub cr/ /0 is connected to infinity by an occupied path in Theta (phi)/, then ..beta..(phi) is strictly decreasing in phi on (0,2..pi..). Similarly, lim/sub n ..-->.. infinity/(-log n)/sup -1/ log p/sub cr/ /0 is connected by an occupied path in Theta(phi) to the exterior of (-n,n) x (-n,n) is strictly decreasing in phi on (0, 2..pi..).
- Research Organization:
- Cornell Univ., NY
- OSTI ID:
- 6317689
- Journal Information:
- J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 46:5/6; ISSN JSTPB
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
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CORRELATION FUNCTIONS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
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MAGNETIC MOMENTS
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