scholarly journals Finite size scaling of the 5D Ising model with free boundary conditions

2014 ◽  
Vol 889 ◽  
pp. 249-260 ◽  
Author(s):  
P.H. Lundow ◽  
K. Markström
Keyword(s):  
Ising Model ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Free Boundary Conditions ◽  
Size Scaling

scholarly journals EXCITATION SPECTRUM AT THE YANG–LEE EDGE SINGULARITY OF 2D ISING MODEL ON THE STRIP

2008 ◽  
Vol 22 (28) ◽  
pp. 4967-4973 ◽  
Author(s):  
SMAIN BALASKA ◽  
JOHN F. MCCABE ◽  
TOMASZ WYDRO
Keyword(s):  
Ising Model ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Excitation Spectrum ◽  
Finite Size ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Edge Singularity ◽  
Free Boundary Conditions ◽  
Conformal Field

At the Yang–Lee edge singularity, finite-size scaling behavior is used to measure the low-lying excitation spectrum of the Ising quantum spin chain for free boundary conditions. The measured spectrum is used to identify the conformal field theory that describes the Yang–Lee edge singularity of the 2D Ising model for free boundary conditions.

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.

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