Critical exponents of plane meanders
  Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We use a recently developed algorithm, based on transfer matrix methods, to enumerate plane meanders. This allows us to calculate the number of closed meanders up to $n=48$, the number of open meanders up to $n=43$, and the number of semi-meanders up to $n=45$. The analysis of the series yields accurate estimates of both the critical point and critical exponent, and shows that a recent conjecture for the exact value of the semi-meander critical exponent is unlikely to be correct, while the conjectured exponent value for closed and open meanders is not inconsistent with the results from the analysis. 
Iwan Jensen and Anthony J Guttmann