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Nuclear Physics B

Integrable boundary Boltzmann weights and surface free energy inversion relations of the chiral Potts model

Yu‐Kui Zhou

Published Jul 1, 1998• 1 citation
Publisher
DOI
10.1016/s0550-3213(98)00231-4

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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.
The finite lattice method is used to derive low-temperature series expansions for surface magnetisations for the 3-state Potts model on the square lattice, for both fixed and free boundary conditions. Combinatorial weights required for surface corrections to the free energy have been generalised to include cases with explicit surface interactions. Analysis of series for the surface correction to the bulk magnetisation is consistent with the generic scaling prediction, assuming a slow convergence comparable to that found in analysis of Potts model series for bulk properties. For free boundaries, analysis of the ordering of the surface layer confirms the specific Potts model result derived from conformal invariance.