Absence of gap for infinite half-integer spin ladders with an odd number of legs

A proof is presented for the absence of gap for spin-1/2 ladders with an odd number of legs in the infinite-leg length limit. This result is relevant to the current discussion of coupled one-dimensional spin systems, a physical realization of which are vanadyl pyrophosphate, (VO)(2)P2O7, and stoichiometric Srn-1Cun+1O2n (with n = 3,5,7,9,...).