Exact finite-size corrections of the free energy for the square lattice dimer model under different boundary conditions

2003 ◽  
Vol 67 (6) ◽  
Author(s):  
N. Sh. Izmailian ◽  
K. B. Oganesyan ◽  
Chin-Kun Hu
Keyword(s):  
Free Energy ◽  
Boundary Conditions ◽  
Finite Size ◽  
Square Lattice ◽  
Dimer Model ◽  
Different Boundary Conditions ◽  
Finite Size Corrections

scholarly journals Anisotropic scaling of the two-dimensional Ising model I: the torus

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Anisotropic Scaling

We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and – if present – the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.

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

scholarly journals Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Finite Lattices ◽  
Antiferromagnetic Ising Model ◽  
Boundary Fields

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.

scholarly journals Finite-size corrections for the attractive mean-field monomer-dimer model

2019 ◽  
Vol 52 (10) ◽  
pp. 105001
Author(s):  
Diego Alberici ◽  
Pierluigi Contucci ◽  
Rachele Luzi ◽  
Cecilia Vernia
Keyword(s):  
Mean Field ◽  
Finite Size ◽  
Dimer Model ◽  
Finite Size Corrections

FINITE SIZE CORRECTIONS IN THE FERROMAGNETIC PHASE OF THE RANDOM ENERGY MODEL

1995 ◽  
Vol 09 (14) ◽  
pp. 877-882 ◽  
Author(s):  
S. ROUHANI ◽  
D. SAAKIAN
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Fine Structure ◽  
Finite Size ◽  
Energy Model ◽  
Ferromagnetic Phase ◽  
Random Energy Model ◽  
Random Energy ◽  
Finite Size Corrections

The ferromagnetic phase of the random energy model was investigated for all values of the parameters. Finite size corrections to the free energy were calculated and the fine structure of the phase diagram, areas with the same size corrections, in the ferromagnetic phase was found.

scholarly journals Finite-size corrections and scaling for the dimer model on the checkerboard lattice

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
Nickolay Sh. Izmailian ◽  
Ming-Chya Wu ◽  
Chin-Kun Hu
Keyword(s):  
Finite Size ◽  
Dimer Model ◽  
Finite Size Corrections
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