Journal of Statistical Physics, Vol. 65, Nos. 1/2, 1991 Ports Model, Dirac Propagator, and Conformational Statistics of Semiflexible Polymers Arkady L. Kholodenko 1 Received August 28, 1990; final March 12, 1991 A new discretized version of the Dirac propagator in d space and one time dimensions is obtained with the help of the 2d-state, one-dimensional Potts model. The Euclidean version of this propagator describes all conformational properties of semiflexible polymers. It also describes all properties of fully directed self-avoiding walks. The case of semiflexible copolymers composed of a random sequence of fully flexible and semirigid monomer units is also considered. As a by-product, some new results for disordered one-dimensional Ising and Potts models are obtained. In the case of the Potts model the non- trivial extension of the results to higher dimensions is discussed briefly. KEY WORDS: Ising model; Potts model; directed self-avoiding walks; Dirac propagator; conformational statistics of semiflexible polymers. 1. INTRODUCTION A simple model of semiflexible polymers which for the fixed polymer length exhibits a rigid-rod to random-coil type of transition has been well known for some time. (1) Only recently (2'3) was it recognized, however, that this model is directly connected with the Euclidean version of Dirac's propagator, so that the rigid-rod to random-coil transition can be associated with the transition from the ultrarelativistic to the nonrelativistic limit of the Dirac propagator. It is well known that the path integrals are well defined if and only if there is some systematic discretization procedure so that the path integrals can be understood as some limits of ordinary multidimensional integrals. In the case of the Dirac propagator there are many ways to write the corresponding path integrals. It is not my purpose to give here the corn- 1 375 H. L. Hunter Laboratories, Clemson University, Clemson, South Carolina 29634-1905. 291 0022-4715/91/1000-0291506.50/0 9 1991 Plenum Publishing Corporation