Regensburg 2000 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 23: Magnetismus und Spinsysteme

DY 23.5: Vortrag

Dienstag, 28. März 2000, 12:15–12:30, H3

Potts models on quasiperiodic graphs — •P. Repetowicz, U. Grimm, and M. Schreiber — Institut für Physik, Technische Universität, 09107 Chemnitz

We consider a q-state Potts model on planar quasiperiodic graphs (QPG) for integer q. We perform a graphical high-temperature expansion of the free energy and investigate the critical behaviour. The expansion involves star graphs consisting of sites with degree larger than one, in other words, ”loops” and their ”fillings” [1], i.e., graphs bounded by a closed loop with all edges belonging exclusively to the region enclosed by the loop. The weight of a graph with l edges and v sites is a polynomial in q which depends on the topology of the graph, in particular on its cyclomatic number c = l−v+1. Star graph topologies with given c have been classified in [2]. The contributing graphs are the same as for the Ising model, hence we can compute the series expansion to the same order as in our previous work on Ising models on QPG [3]. We investigate the influence of quasiperiodic order on the phase transition. In particular, we want to ascertain whether the change from a second-order to a first-order phase transition, occuring on the square lattice for q>4, still takes place on QPG. The results are compared with Monte Carlo simulations of a q=3 Potts model on the octagonal tiling [4].

[1] F. Y. Wu, Rev. of Mod. Phys. 54 (1982) 235

[2] C. Domb, Phase Transitions and Critical Phenomena vol 3, pp. 1–42

[3] P. Repetowicz, U. Grimm, M. Schreiber, J. Phys. A 32 (1999) 4397

[4] D. Ledue, T. Boutry, D.P. Landau, J. Teillet, Phys. Rev. B 56 (1997) 10782