Enumeration of self-avoiding trails on a square lattice using a transfer matrix technique

Abstract

The authors describe a new algebraic technique, utilizing transfer matrices, for enumerating self-avoiding trails on the square lattice. They have enumerated trails to 31 steps, and find increased evidence that trails are in the self-avoiding walk universality class. Assuming that trails behave like A lambda nn1132/, they find lambda =2.72062+or-0.000006 and A=1.272+or-0.002.