The Reggeon quantum spin (RQS) model on the transverse lattice in D dimensional impact parameter space has been conjectured to have the same critical behaviour as the Reggeon field theory (RFT). Thus from a high “temperature” series of ten ( D = 2) and twenty ( D = 1) terms for the RQS model we extrapolate to the critical temperature T = T c by Padé approximants to obtain the exponents η=0.238±0.008, z=1.16±0.01, v=1.271±0.007 for D=2 and η=0.317±0.002, z=1.272±0.007, v=1.736±0.001, λ=0.57±0.03 for D=1. These exponents naturally interpolate between the D=0 and D=4− ε results for RFT as expected on the basis of the universality conjecture.