scholarly journals Perturbative renormalization group, exact results, and high-temperature series to order 21 for theN-vector spin models on the square lattice

1996 ◽  
Vol 54 (22) ◽  
pp. 15828-15848 ◽  
Author(s):  
P. Butera ◽  
M. Comi
Keyword(s):  
Renormalization Group ◽  
High Temperature ◽  
Temperature Series ◽  
Square Lattice ◽  
Exact Results ◽  
Spin Models ◽  
Perturbative Renormalization ◽  
Vector Spin Models

Some exact results for the Ashkin-Teller model

1979 ◽  
Vol 365 (1722) ◽  
pp. 371-380 ◽  
Keyword(s):  
Renormalization Group ◽  
Partition Function ◽  
Potts Model ◽  
Critical Line ◽  
Square Lattice ◽  
Direct Connection ◽  
Exact Results ◽  
Renormalization Group Theory ◽  
Vertex Model ◽  
Special Cases

It is shown that various cases of the Ashkin-Teller model on the square, triangular and hexagonal lattices can be transformed by the dual and star-triangle transformations and, further, that these problems can be reduced to special cases of the eight vertex model on the Kagomé lattice. In general, we can only obtain the partition function of the Ashkin-Teller model if we are on its line of fixed points, and it then turns out that it is reducible to the six vertex model. Since the partition function of the q -state Potts model at its critical point can also be related to the six vertex model, a direct connection between the Ashkin-Teller model and the Potts model can be made. It turns out that moving along the critical line of the Ashkin-Teller model corresponds to varying q for the Potts model. For the square lattice comparison is made with renormalization group calculations, and the agreement found is a satisfactory check of renormalization group theory.

scholarly journals Thermal tensor renormalization group simulations of square-lattice quantum spin models

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Han Li ◽  
Bin-Bin Chen ◽  
Ziyu Chen ◽  
Jan von Delft ◽  
Andreas Weichselbaum ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Quantum Spin ◽  
Square Lattice ◽  
Spin Models ◽  
Lattice Quantum ◽  
Quantum Spin Models
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