Critical behaviour of the 1D q-state Potts model with long-range interactions

The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as r-(1+ sigma has been studied in the wide range of parameters 0< sigma <or=1 and 1/16 <or=q<or=64. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented.