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 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

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

scholarly journals Finite-size corrections for universal boundary entropy in bond percolation

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Jan de Gier ◽  
Jesper Jacobsen ◽  
Anita Ponsaing
Keyword(s):  
Field Theory ◽  
Arbitrary Order ◽  
Finite Size ◽  
Square Lattice ◽  
Bond Percolation ◽  
Exact Results ◽  
Conformal Field ◽  
Logarithmic Corrections ◽  
Special Value ◽  
Finite Size Corrections

We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size LL. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finite-size corrections to arbitrary order. For the strip we provide exact expressions that have been verified using high-precision numerical analysis. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

Sign in / Sign up

Export Citation Format

Share Document