The Nearest-Neighbor Self-Avoiding Walk with Complex Killing Rates

Abstract

The Green's function for the nearest-neighbor self-avoiding walk on a hypercubic lattice in d > 2 dimensions is constructed and shown to be analytic for values of the killing rate a ∈ C satisfying |a| > , | arg a| < 3π/4 − b with > 0 and 0 < b < π/4. We restrict |a| > > 0 in order to use the killing rate as an infrared cutoff, which allows us to construct Green's function using a single scale cluster expansion. The presence of non-real killing introduces complications that we resolve through the use of an appropriate choice of decoupling scheme and a subsidiary expansion. Our methods can be used to control a single momemtum slice in a phase-space expansion.