Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-04-14
J. Phys. A 33 No. 40 (2000), 7053
Physics
Condensed Matter
Statistical Mechanics
16 pages. revised: references added. revised 08/00: last part slightly expanded
Scientific paper
10.1088/0305-4470/33/40/304
We address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for the partition function with domain wall boundary conditions, we derive Toda differential equations and solve them asymptotically in order to extract the bulk free energy. We find that it is different and bears no simple relation with the free energy for periodic boundary conditions. The six vertex model with domain wall boundary conditions is closely related to algebraic combinatorics (alternating sign matrices). This implies new results for the weighted counting for large size alternating sign matrices. Finally we comment on the interpretation of our results, in particular in connection with domino tilings (dimers on a square lattice).
Korepin Vladimir
Zinn-Justin Paul
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