We consider the critical behavior of the susceptibility of the self-avoiding walk on the graph T×Z, where T is a Bethe lattice with degree k and Z is the one dimensional lattice. By directly estimating the two-point function using a method of Grimmett and Newman, we show that the bubble condition is satisfied when k>2, and therefore the critical exponent associated with the susceptibility equals 1.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics