We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a universal amplitude.
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|Publication status||Published - 1 Jan 2004|
- critical exponents and amplitudes (theory)
- finite-size scaling
- phase diagrams (theory)
- series expansions