Convex lattice polygons of fixed area with perimeter dependent weights

Details Convex lattice polygons of fixed area with perimeter dependent weights Convex lattice polygons of fixed area with perimeter dependent weights

2003-03-27

arxiv.org/abs/cond-mat/0303577v1

Physical Review E, Vol 71, 016130 (2005)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures, revtex4

Scientific paper

10.1103/PhysRevE.71.016130

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight t^m to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s^{-theta_{conv}} exp[K s^(1/2)] for large s and t less than a critical threshold t_c, where K is a t-dependent constant, and theta_{conv} is a critical exponent which does not change with t. We find theta_{conv} is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected non-universality of theta_{conv} is traced to existence of sharp corners in the asymptotic shape of these polygons.

Affiliated with

Also associated with

No associations

Rating

Convex lattice polygons of fixed area with perimeter dependent weights does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convex lattice polygons of fixed area with perimeter dependent weights, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convex lattice polygons of fixed area with perimeter dependent weights will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-132665