@article{oai:nagoya.repo.nii.ac.jp:00010206, author = {Minami, Kazuhiko}, journal = {JOURNAL OF MATHEMATICAL PHYSICS}, month = {Mar}, note = {The free energies of six-vertex models on a general domain D with various boundary conditions are investigated with the use of the n-equivalence relation, which help classify the thermodynamic limit properties. It is derived that the free energy of the six-vertex model on the rectangle is unique in the limit (height,width)->(∞,∞). It is derived that the free energies of the model on the domain D are classified through the densities of left/down arrows on the boundary. Specifically, the free energy is identical to that obtained by Lieb [Phys. Rev. Lett. 18, 1046 (1967); 19, 108 (1967); Phys. Rev. 162, 162 (1967)] and Sutherland [Phys. Rev. Lett 19, 103 (1967)] with the cyclic boundary condition when the densities are both equal to 1/2. This fact explains several results already obtained through the transfer matrix calculation. The relation to the domino tiling (or dimer, or matching) problems is also noted.}, pages = {033514--033514}, title = {The free energies of six-vertex models and the n-equivalence relation}, volume = {49}, year = {2008} }