Specific heat and partition function zeros for the dimer model on the checkerboard B lattice: Finite-size effects

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Mathematical Physics

Background:

• Dimer models on lattices exhibit diverse critical behaviors.
• Checkerboard lattices A, B, and C present distinct properties.
• Checkerboard B and C lattices show richer critical phenomena than A.

Purpose of the Study:

• To thoroughly investigate the dimer model on checkerboard B lattices.
• To analyze the partition function and specific heat behavior.
• To understand the impact of lattice anisotropy on critical properties.

Main Methods:

• Analysis of the partition function for a 2M×2N checkerboard B lattice on a torus.
• Examination of partition function zeros and specific heat.
• Investigation of lattice anisotropy effects on correlation length and shift exponents.

Main Results:

• The dimer model on checkerboard B lattices exhibits two critical behaviors.
• Partition function zeros display complex structures (rings, circles, arabesques).
• Specific heat peaks and zero circles increase with system size; lattice anisotropy affects critical exponents (λ ≠ 1/ν).

Conclusions:

• The dimer model on checkerboard B lattices presents unique critical phenomena.
• Partition function zeros and specific heat reveal intricate system-size dependencies.
• Lattice anisotropy plays a crucial role in determining the model's critical behavior and exponents.