A self-avoiding walk on random strips

International audienceTo describe a polymer in a random medium, the author considers a self-avoiding walk (SAW) on a lattice whose bonds are randomly favourable (with probability 1-p) or unfavourable (with probability p). The size of a SAW of N steps is calculated when the lattice is a strip by performing products of random matrices. When the weight of unfavourable bonds tends to 0, there exist critical concentrations p c where the size of the SAW undergoes first-order transitions. The origin of these transitions is explained as well as the fact that the limits p to 0 or p to 1 are discontinuous. Possible consequences for higher-dimensional systems are discussed