Strict inequalities for some critical exponents in two-dimensional perclation

Journal Article · Sun Mar 01 04:00:00 EST 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01011155· OSTI ID:6317689

Kesten, H; Zhang, Yu

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

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CORRELATION FUNCTIONS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
FERROMAGNETISM
FUNCTIONS
MAGNETIC MOMENTS
MAGNETISM
MAPPING
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
MECHANICS
ORDER PARAMETERS
PROBABILITY
SCALING LAWS
SPIN GLASS STATE
STATISTICAL MECHANICS
TOPOLOGICAL MAPPING
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS