Static critical behavior of the ferromagnetic Ising model on the quasiperiodic octagonal tiling

1995 ◽  
Vol 51 (18) ◽  
pp. 12523-12530 ◽  
Author(s):  
D. Ledue ◽  
D. P. Landau ◽  
J. Teillet
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Ferromagnetic Ising Model

FRUSTRATION EFFECTS ON SMALL-WORLD NETWORKS

2004 ◽  
Vol 15 (09) ◽  
pp. 1269-1277 ◽  
Author(s):  
PAULO R. A. CAMPOS ◽  
VIVIANE M. DE OLIVEIRA ◽  
F. G. BRADY MOREIRA
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Critical Behavior ◽  
Magnetic Ordering ◽  
Small World ◽  
Two Dimensions ◽  
Small World Networks ◽  
Ferromagnetic Ising Model ◽  
Antiferromagnetic Ising Model ◽  
Frustration Effects

We investigate the frustration effects on small-world networks by studying antiferromagnetic Ising model in two dimensions. When the rewiring is constrained to those sites such that the interaction still occurs between spins in distinct sublattices and frustration does not take place, we observe that the system behaves as in previous investigations of ferromagnetic Ising model. However, when the rewiring procedure does not only produce interactions between spins in distinct sublattices, small-world configurations can effectively produce geometrical frustration and we attain a different critical behavior. In the frustrated case, the critical temperature decreases with the augment of the rewiring probability and the magnetic ordering presents two different regimes for low and high p.

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 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.

Critical behavior near a smooth inhomogeneity in the planar Ising model and conformal invariance

1990 ◽  
Vol 65 (14) ◽  
pp. 1773-1776 ◽  
Author(s):  
Ferenc Iglói ◽  
Bertrand Berche ◽  
Loïc Turban
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Conformal Invariance

Critical behavior of an Ising model on a cubic compressible lattice

1976 ◽  
Vol 13 (5) ◽  
pp. 2145-2175 ◽  
Author(s):  
D. J. Bergman ◽  
B. I. Halperin
Keyword(s):  
Ising Model ◽  
Critical Behavior
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