The "inversion relation" method for obtaining the free energy of the chiral Potts model

Details The "inversion relation" method for obtaining the free energy of the chiral Potts model The "inversion relation" method for obtaining the free energy of the chiral Potts model

2002-12-03

arxiv.org/abs/cond-mat/0212075v1

Physica A322 (2003) 407-431

Physics

Condensed Matter

Statistical Mechanics

27 pages, 4 figures

Scientific paper

10.1016/S0378-4371(02)02024-1

We derive the free energy of the chiral Potts model by the infinite lattice ``inversion relation'' method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that in addition to the usual assumption that the free energy be analytic and bounded in some principal domain of the rapidity parameter space that includes the physical regime, we also need a much less obvious symmetry. We can then obtain the free energy by Wiener-Hopf factorization in the complex planes of appropriate variables. Together with the inversion relation, this symmetry relates the values of the free energy in all neighbouring domains to those in the principal domain.

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