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Dimer model on a triangular lattice.
1Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan. izmailan@phys.sinica.edu.tw
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2011
Summary
We analyzed the dimer model on a triangular lattice. Its critical behavior is described by conformal field theory, with specific heat depending on lattice size parity.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Conformal Field Theory
Background:
- The dimer model is a fundamental system in statistical mechanics.
- Understanding its behavior on toroidal lattices is crucial for theoretical physics.
Purpose of the Study:
- Analyze the partition function of the dimer model on an M×N triangular lattice on a torus.
- Investigate the impact of lattice size parity on critical behavior.
Main Methods:
- Finite-size analysis of the dimer model's partition function.
- Application of conformal field theory to describe the model's critical properties.
Main Results:
- The dimer model on this lattice is described by a conformal field theory with central charge c=-2.
- The shift exponent (λ) for specific heat depends on the parity of N.
- For odd N, λ=1, leading to a size-dependent pseudocritical point.
- For even N, λ=∞, where the pseudocritical point aligns with the thermodynamic critical point.
Conclusions:
- The parity of lattice sites significantly influences the finite-size scaling of the dimer model.
- Conformal field theory provides an effective description of the dimer model's critical phenomena on a torus.
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