Real-space renormalization group approach to the Potts model on the two-dimensional Penrose tiling

Gang Xiong, Zhe-Hua Zhang and De-Cheng Tian

Physica A: Statistical Mechanics and its Applications, 1999, vol. 265, issue 3, 547-556

Abstract: A one-step real-space renormalization group (RSRG) transformation is used to study the q-state Potts model on the two-dimensional (2D) Penrose tiling (PT). The critical exponents of the correlation length ν(q) in the region between q=1 and q=4 are obtained. The bond percolation (BP) threshold and Ising critical temperature in the isotropic case are also obtained. The comparison of the results with previous results on the PT and the exact results on square lattice (SQL) indicates that the universal classes of q-state Potts model on PT and SQL may be the same.

Keywords: One-step real-space renormalization group; q-state Potts model; Critical exponents; Bond percolation threshold; Ising critical temperature (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:265:y:1999:i:3:p:547-556

DOI: 10.1016/S0378-4371(98)00647-5

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