Correlation Lengths for Oriented Percolation

We begin by descr ib ing the mode l under cons idera t ion . Let 5 0 = { ( m , n ) e 2 2 : m + n is even} and make 50 into a g raph by d rawing an or iented arc from each z ~ 5 ~ to z + (1, 1 ) and to z + ( 1, l ). Each arc, also called a bond, is independen t ly open with p robab i l i t y p and closed with p robab i l i t y 1 p. An open b o n d indicates that flow is a l lowed in the direct ion of the or ienta t ion . Wi th this in mind, we write x--+ y (and say y can be reached f rom x) if there is an open pa th f rom x to y, i.e., there is a sequence of sites in 50, x = x0, xl, . . . , xn = y, so tha t for each m ~<n the arc from Xm_ 1 to Xm is open. Th ink ing of the vert ical d i rec t ion as time, we set