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Bethe ansatz solution of triangular trimers on the triangular lattice.
1Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.
Summary
This study details the exact calculation for a triangular trimer model on a triangular lattice. The findings provide a complete solution for its free energy using a coordinate Bethe ansatz.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Mathematical Physics
Background:
- A model of triangular trimers on a triangular lattice was recently introduced.
- The exact free energy for this model was previously stated but not fully derived.
Purpose of the Study:
- To present the complete mathematical derivation for the exact free energy of the triangular trimer model.
- To elucidate the solution methodology involving the coordinate Bethe ansatz.
Main Methods:
- Utilizing a coordinate Bethe ansatz with two distinct particle types.
- Drawing parallels with the solution of the square-triangle random tiling model.
Main Results:
- The complete calculation leading to the exact free energy of the triangular trimer model is presented.
- The solution is shown to be analogous to that of the square-triangle random tiling model.
Conclusions:
- The exact solution for the triangular trimer model's free energy is rigorously derived.
- The study highlights connections between the trimer model and other solvable statistical mechanics models.