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

Abstract

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 $0<\sigma \le 1$ and $\frac{1}{16}\le q\le 64$. 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.

20 pages plus 4 figures, Latex

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