Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

Details Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

1997-03-06

arxiv.org/abs/cond-mat/9703065v1

Phys. Rev. E 56, 3999 (1997)

Physics

Condensed Matter

Statistical Mechanics

22 pages in Revtex, 6 PS files, submitted to PRE

Scientific paper

10.1103/PhysRevE.56.3999

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.

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