The histogram characteristics of perimeter polynomials for directed percolation

New perimeter polynomials (in dimensions d=2 to 4) are analysed for directed site percolation. A study of these data shows that i) above p c the average perimeter-to-size ratio varies as a=(1−p)/p+Bs −1/d ; ii) At p c its leading correction term estimates supports the prediction (from scaling) of an exponent equal to 1/Δ−1 (with Δ the gap exponent for directed percolation); iii) At p=0 the limiting ratio is estimated on various lattices. Fairly definitive evidence is obtained in favour of a(p=0)=3/4 for the square site animals and this result is used to study the second correction term which is estimated to be analytic (∼s −2 ) as the first correction term (Bethe-like and s −1 , without any obvious dimensional dependence) On analyse de nouveaux polynomes de perimetre (d=2 a 4) dans le cas de la percolation de site orientee. On trouve que: 1) au-dessus de p c , le rapport moyen perimetre sur taille varie comme a=(1-p)/p+Bs −1/d ; 2) a p c , l'evaluation du terme de correction dominant corrobore la prediction d'un exposant egal a 1/Δ−1 (ou Δ est l'exposant du saut de percolation orientee; 3) a p=0 on estime la limite du rapport pour plusieurs reseaux. On obtient des resultats assez concluants en faveur de a(p=0)=3/4 pour les animaux de site sur reseau carre et a partir de la on estime le second terme de correction. On le trouve analytique (∼s −2 ) comme le premier terme (du type de Bethe ∼5 −1 , et apparemment independant de la dimension)