Classical lattice models with single-node interactions on hierarchical lattices: The two-layer Ising model

2020 ◽  
Vol 558 ◽  
pp. 124919
Author(s):  
A.V. Myshlyavtsev ◽  
M.D. Myshlyavtseva ◽  
S.S. Akimenko
Keyword(s):  
Ising Model ◽  
Lattice Models ◽  
Classical Lattice ◽  
Single Node ◽  
Hierarchical Lattices

LATTICE ALGEBRAS AND THE HIDDEN SYMMETRY OF THE 2D ISING MODEL IN A MAGNETIC FIELD

1991 ◽  
Vol 06 (28) ◽  
pp. 5127-5153 ◽  
Author(s):  
DAN LEVY
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Lattice Models ◽  
Natural Generalization ◽  
Xxz Model ◽  
Affine Hecke Algebra ◽  
Finite Dimensional ◽  
Hidden Symmetry ◽  
Boundary Terms

Lattice algebras are defined and used to study the symmetries of 2D lattice models. New and interesting examples of such algebras are provided by the affine Hecke algebra, owing to the possibility of constructing braid generators out of its generators. I propose an Ansatz for the braid generators and derive some solutions. A particular finite-dimensional quotient is shown to be a natural generalization of the Temperley-Lieb-Jones algebra. It is used to give a unified picture of known and unknown symmetries of the spin-½ xxz model with boundary terms. The Ising model in an external magnetic field is also a representation of this quotient.

Free-fermion, checkerboard and Z -invariant lattice models in statistical mechanics

1986 ◽  
Vol 404 (1826) ◽  
pp. 1-33 ◽  
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Three Dimensional ◽  
Lattice Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Local Correlations ◽  
Free Fermion Model ◽  
Zamolodchikov Model ◽  
Special Case

It is shown that the two-dimensional free fermion model is equivalent to a checkerboard Ising model, which is a special case of the general ‘ Z -invariant’ Ising model. Expressions are given for the partition function and local correlations in terms of those of the regular square lattice Ising model. Corresponding results are given for the self-dual Potts model, and the application of the methods to the three-dimensional Zamolodchikov model is discussed. The paper ends with a discussion of the critical and disorder surfaces of the checkerboard Potts model.

scholarly journals Dual geometric worm algorithm for two-dimensional discrete classical lattice models

2004 ◽  
Vol 70 (1) ◽  
Author(s):  
Peter Hitchcock ◽  
Erik S. Sørensen ◽  
Fabien Alet
Keyword(s):  
Lattice Models ◽  
Two Dimensional ◽  
Classical Lattice

scholarly journals Quantum algorithms for classical lattice models

2011 ◽  
Vol 13 (9) ◽  
pp. 093021 ◽  
Author(s):  
G De las Cuevas ◽  
W Dür ◽  
M Van den Nest ◽  
M A Martin-Delgado
Keyword(s):  
Quantum Algorithms ◽  
Lattice Models ◽  
Classical Lattice

scholarly journals Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

2005 ◽  
Vol 74 (Suppl) ◽  
pp. 111-114 ◽  
Author(s):  
Kouji Ueda ◽  
Ryota Otani ◽  
Yukinobu Nishio ◽  
Andrej Gendiar ◽  
Tomotoshi Nishino
Keyword(s):  
Renormalization Group ◽  
Transfer Matrix ◽  
Lattice Models ◽  
Classical Lattice

scholarly journals Transfer matrix approach to the disordered Ising model on hierarchical lattices

2006 ◽  
Vol 73 (17) ◽  
Author(s):  
Danielle O. C. Santos ◽  
Edvaldo Nogueira ◽  
Roberto F. S. Andrade
Keyword(s):  
Ising Model ◽  
Transfer Matrix ◽  
Matrix Approach ◽  
Transfer Matrix Approach ◽  
Hierarchical Lattices
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