Density of Yang–Lee zeros and Yang–Lee edge singularity for the antiferromagnetic Ising model

2005 ◽  
Vol 705 (3) ◽  
pp. 504-520 ◽  
Author(s):  
Seung-Yeon Kim
Keyword(s):  
Ising Model ◽  
Edge Singularity ◽  
Antiferromagnetic Ising Model

scholarly journals Lee-Yang zeros of the antiferromagnetic Ising model

2021 ◽  
pp. 1-35
Author(s):  
FERENC BENCS ◽  
PJOTR BUYS ◽  
LORENZO GUERINI ◽  
HAN PETERS
Keyword(s):  
Ising Model ◽  
Partition Functions ◽  
Cayley Trees ◽  
Circular Arcs ◽  
Precise Characterization ◽  
Ferromagnetic Ising Model ◽  
Location Of Zeros ◽  
Antiferromagnetic Ising Model ◽  
Recursively Defined Trees ◽  
Degree Bound

Abstract We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

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 Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 780
Author(s):  
Liang-Jun Zhai ◽  
Guang-Yao Huang ◽  
Huai-Yu Wang
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Behavior ◽  
Critical Region ◽  
Numerical Study ◽  
Transverse Field ◽  
Scaling Theory ◽  
New Order ◽  
Edge Singularity ◽  
Transverse Field Ising Model

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

scholarly journals Analysis of a long-range random field quantum antiferromagnetic Ising model

2006 ◽  
Vol 51 (3) ◽  
pp. 321-329 ◽  
Author(s):  
B. K. Chakrabarti ◽  
Arnab Das ◽  
Jun-ichi Inoue
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Long Range ◽  
Antiferromagnetic Ising Model

Phase diagram of the dilute antiferromagnetic Ising model

1998 ◽  
Vol 244 (1-3) ◽  
pp. 165-168 ◽  
Author(s):  
E.E. Reinehr ◽  
W. Figueiredo
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Antiferromagnetic Ising Model
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