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Physics Letters A

Percolation renormalisation group method and its application to the Potts model

Chin‐Kun Hu, Chi-Ning Chen

Published Jul 1, 1988• 9 citations
Publisher
DOI
10.1016/0375-9601(88)90704-9

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The Legendre transformation, a modification of the decimation method used in the real space renormalisation group, is employed to study the critical behaviour of the two-dimensional S-state Potts model which exhibits a second-order phase transition for S<or=4. Thermal and magnetic critical exponents are calculated for the percolation (S to 1), Ising (S=2) and three- and four-state Potts models. Decimation estimates of the critical exponents and critical points for S=2, 3 and 4 are also presented.
A renormalisation group approach developed for the percolation problem by Young and Stinchcombe (1975) is extended to yield magnetic indices. A real-space cluster calculation is carried out for the Ashkin-Teller-Potts model (Ashkin & Teller 1964, Potts 1952) with general S, allowing contact with results for the Ising model (S to 2) as well as with the previously published thermal indices of the percolation problem (S to 1). For the percolation problem, the magnetic index obtained is 2.06, about 10% larger than current series estimates, and results in gamma =2.87.