Distribution of Transverse Distances in Directed Animals

Details Distribution of Transverse Distances in Directed Animals Distribution of Transverse Distances in Directed Animals

2003-03-21

arxiv.org/abs/cond-mat/0303450v1

J. Phys. A:Math. Gen.,Vol 36,3701(2003)

Physics

Condensed Matter

Statistical Mechanics

10 latex pages,1 eps-figure

Scientific paper

10.1088/0305-4470/36/13/305

We relate $\phi(\bf{x},s)$, the average number of sites at a transverse distance $\bf{x}$ in the directed animals with $s$ sites in $d$ transverse dimensions, to the two-point correlation function of a lattice gas with nearest neighbor exclusion in $d$ dimensions. For large $s$, $\phi(\bf{x},s)$ has the scaling form $\frac{s}{R_s^d} f(|\bf{x}|/R_s)$, where $R_s$ is the root mean square radius of gyration of animals of $s$ sites. We determine the exact scaling function for $d =1$ to be $f(r) = \frac{\sqrt{\pi}}{2 \sqrt{3}}erfc(r/\sqrt{3})$. We also show that $\phi(\bf{x}=0,s)$ can be determined in terms of the animals number generating function of the directed animals.

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