Specific Heat and Partition Function Zeros for the Dimer Model on the Checkerboard B Lattice: Finite-Size Effects

Chi-Ning Chen^1*, Chin-Kun Hu^1,2, N. Sh. Izmailian³, Ming-Chya Wu^2,4

¹Department of Physics, National Dong-Hwa University, Hualien, Taiwan
²Institute of Physics, Academia Sinica, Taipei, Taiwan
³Yerevan Physics Institute, Yerevan state University, Yerevan, Armenia
⁴Research Center for Adaptive Data Analysis, National Central University, Taoyuan, Taiwan

* Presenter:Chi-Ning Chen, email:cnchen@gms.ndhu.edu.tw

There are three possible classifications of the dimer weights on the bonds of the checkerboard lattice and they
are denoted as checkerboard A, B and C lattices. The dimer model on the checkerboard B and C lattices has
much richer critical behavior comparing with the dimer model on the checkerboard A lattice. In this paper, we
study in full details the dimer model on the checkerboard B lattice. The dimer model on the checkerboard B
lattice has two types of the critical behaviors associated with different universality classes, namely c = −2 and
c = 1. In one limit, this model is the anisotropic dimer model on the rectangular lattice with an algebraic decay of
correlators, and in another limit, it is the anisotropic generalized Kasteleyn model with radically different critical
behavior. We analyze the partition function of the dimer model on a 2M ×2N checkerboard B lattice wrapped
on a torus obtained by Izmailian, Hu and Kenna [Phys. Rev. E 91, 062139 (2015)]. We find that for this lattice
the correlation length exponent ν is unequal to the shift exponent λ (ν 6= λ). We also find the very unusual behavior
of the partition function zeros and the specific heat of the dimer model. Remarkably, we find out that the number
of the specific heat peaks and the number of the circle of the partition function zeros increases with the system
size. We investigate the properties of the specific heat and partition function zeros near the critical point.

Keywords: dimer model, Kasteleyn Transition, partition function zeros, shift exponent, finite-size effect