Finite-size corrections for the free energy of the two-sublattice vertex model

Chris J. Hamer

R. Z. Bariev, Trong Tuong Truong

R. Z. Bariev

M. Karowski

Wenfei Li, Hyunggyu Park, Michael Widom

The authors study finite-size corrections to the free energy in a two-dimensional random tiling model. This model is equivalent to an asymmetric six-vertex model and exhibits commensurate-incommensurate phase transitions of the Pokrovsky-Talapov type. They calculate finite-size scaling amplitudes of the free energy inside the incommensurate phase, analytically and numerically, by employing a transfer matrix method. Both periodic and free boundary conditions are considered. These amplitudes are consistent with predictions of the theory of conformal invariance with the conformal charge c=1.

R. Z. Bariev, Trong Tuong Truong, Loïc Turban

The exact diagonalization of the diagonal-to-diagonal transfer matrix of an N-sublattice vertex model with interactions of the vertex-arrow type between sublattices is carried out using the generalized nested Bethe-ansatz method. An exact expression for the free energy is obtained involving the solution of an integral equation which is studied numerically.