Percolation, the specialFTHETA’ point, and theFTHETA-FTHETA’ universality puzzle

Results for d=2 percolation allow one to determine exactly the critical exponents for a polymer undergoing the special surface transition, while its bulk is at the FTHETA’ point. ${\gamma }_1$=8/7 and ${\mathrm{\phi }}_{\mathit{s}}$=8/21 are the entropic and the crossover surface exponents, respectively. On the other hand, exact enumerations analysis leads to conjecture ${\gamma }_1$=4/7 at an ordinary FTHETA’ point. This strongly supports universality of FTHETA and FTHETA’ points. Similar exact results are obtained for a multicritical walk in the presence of correlated percolation vacancies.