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 EXCITATION SPECTRUM AT THE YANG–LEE EDGE SINGULARITY OF THE 2D ISING MODEL

2006 ◽  
Vol 20 (04) ◽  
pp. 495-504 ◽  
Author(s):  
JOHN F. MCCABE ◽  
TOMASZ WYDRO
Keyword(s):  
Ising Model ◽  
Excitation Spectrum ◽  
Spin Chain ◽  
Central Charge ◽  
Finite Size ◽  
Quantum Spin ◽  
Finite Size Scaling ◽  
Quantum Spin Chain ◽  
Edge Singularity ◽  
Conformal Field

This paper studies the Yang–Lee edge singularity of 2-dimensional (2D) Ising model through a quantum spin chain. In particular, finite-size scaling measurements on the quantum spin chain are used to determine the low-lying excitation spectrum and central charge at the Yang–Lee edge singularity. The measured values are consistent with predictions for the (A4, A1) minimal conformal field theory.

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 BETHE ANSATZ SOLUTIONS FOR TEMPERLEY–LIEB QUANTUM SPIN CHAINS

2000 ◽  
Vol 15 (21) ◽  
pp. 3395-3425 ◽  
Author(s):  
R. C. T. GHIOTTO ◽  
A. L. MALVEZZI
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Quantum Group ◽  
Bethe Ansatz ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Free Boundary Conditions

We solve the spectrum of quantum spin chains based on representations of the Temperley–Lieb algebra associated with the quantum groups [Formula: see text] for Xn=A1, Bn, Cn and Dn. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

Sign in / Sign up

Export Citation Format

Share Document