scholarly journals Interacting double dimer model on the square lattice

2020 ◽  
Vol 102 (17) ◽  
Author(s):  
Neil Wilkins ◽  
Stephen Powell
Keyword(s):  
Square Lattice ◽  
Dimer Model

scholarly journals Odd–even effect of melting finite polymer film on square lattice

2015 ◽  
Vol 29 (09) ◽  
pp. 1550062
Author(s):  
Tieyan Si
Keyword(s):  
Melting Temperature ◽  
Three Dimensional ◽  
Mathematical Physics ◽  
Finite System ◽  
Square Lattice ◽  
Finite Width ◽  
Two Dimensional ◽  
Dimer Model ◽  
Physics Model ◽  
Straightforward Extension

Two-dimensional film system bears many exotic thermodynamics behaviors. We proposed a mathematical physics model to explore how the melting temperature of a two-dimensional mathematical dimer film depends on the odd–evenness of the finite width of dimer film. A weak external bond between dimers is introduced into the classical dimer model in this dimer film. We derived a general equation of melting temperature and applied it for computing the melting temperature of a dimer film covering a finite square lattice. The melting temperature is proportional to the external bonding energy that we assume it binds neighboring dimers together and proportional to the inverse of entropy per site. Furthermore, it shows fusing two small rectangular dimer film with odd number of length into one big rectangular film gains more entropy than fusing two small rectangles with even number of length into the same big rectangle. Fusing two small toruses with even number of length into one big torus reduces entropy. Fusing two small toruses with odd number of length increases the entropy. Thus two dimer films with even number of length repel each other, two dimer films with odd length attract each other. The odd–even effect is also reflected on the correlation function of two topologically distinguishable loops in a torus surface. The entropy of finite system dominates odd–even effect. This model has straightforward extension to longer polymers and three-dimensional systems.

scholarly journals Exact finite-size corrections in the dimer model on a planar square lattice

2019 ◽  
Vol 52 (33) ◽  
pp. 335001 ◽  
Author(s):  
Nikolay Sh Izmailian ◽  
Vladimir V Papoyan ◽  
Robert M Ziff
Keyword(s):  
Finite Size ◽  
Square Lattice ◽  
Dimer Model ◽  
Finite Size Corrections
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