Extended Universality in Potts Models on Square and Triangular Lattices

It has been recently discovered [1] that some families of systems exhibit universal behavior both near and away from any critical point. Specifically, it has been shown that all thermodynamic observables of the p-state Potts model on a square lattice collapse to the values of the 2-D planar XY model above a certain ``extended universality'' temperature $T_{eu}$ [1]. We have extended these results to the Potts model on triangular and honeycomb lattices. We hypothesize that such sharp transition between discrete and continuous behavior of the observables is due to a Nyquist-Shannon type theorem for statistical mechanics. We present evidence for this interpretation and discuss its relevance to emergent systems. \\[4pt] [1] {\em Universality away from critical points in two-dimensional phase transitions}; C.M. Lapilli, P. Pfeifer, and C. Wexler; Phys. Rev. Lett. {\bf 96}, 140603 (2006).