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

TL;DR

This paper investigates the critical behavior of a one-dimensional q-state Potts model with long-range interactions decaying as r^{-(1+σ)}, analyzing phase diagrams and critical exponents across various parameters.

Contribution

It introduces a transfer matrix approach for a truncated interaction range and applies finite range scaling to study the model's phase diagram and critical exponents.

Findings

Phase diagram mapped across parameters q and σ.

Critical exponent for correlation length determined.

Transfer matrix method effective for 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.