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Physical review. B, Condensed matter

Ferromagnetism and antiferromagnetism in the Potts model in (1 + 1) and (2 + 1) dimensions

L.N. Epele, Huner Fanchiotti A, Carlos A. García Canal

Published Feb 1, 1982• 4 citations
Publisher

Abstract

A previously proposed renormalization-group realization is applied to the $q$-state Potts model for any $q$ in (1 + 1)- and (2 + 1)-dimensional lattices of different coordination number. Ferromagnetic and antiferromagnetic critical points are found and the corresponding exponents are computed in a very simple way.

DOI
10.1103/physrevb.25.1997

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A previously proposed renormalization-group realization is applied to the qqq-state Potts model for any qqq in (1 + 1)- and (2 + 1)-dimensional lattices of different coordination number. Ferromagnetic and antiferromagnetic critical points are found and the corresponding exponents are computed in a very simple way.
The real-space renormalization group theory using the first order cumulant is applied to the q -state antiferromagnetic Potts model on 2-d (dimensional) and 3-d lattice. The special features of this paper are that the Potts states are represented by q unit vectors in q -1 dimensional space and the two-sublattice structure is preserved after the renormalization transformation. The critical exponents obtained for q =2 in 3-d are in fairly good agreement with the reliable values and those for q =3 and 4 are obtained for the first time.
We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be T c = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.
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