Abstract
For a solvable N -state vertex model in the low-temperature antiferroelectric phase, exact per-site free-energy f is calculated as a function of the order-parameter p (`vertical polarization'), based on the quantum inverse scattering method. The Bethe-ansatz integral equation is solved as an expansion with respect to p , which leads to the Gruber-Mullins-Pokrovsky-Talapov-type expansion, f ( p )= f (0)+ a ·| p |+ b ·| p | 3 + O (| p | 4 ). It is found that the coefficients a and b are identical to those of the six-vertex model ( N =2 case). This fact gives support for the universal Gaussian curvature jump for the N -state vertex model interpreted as a model of interface roughening.
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