Decimation transformations in high-temperature renormalization-group methods

1987 ◽  
Vol 65 (3) ◽  
pp. 208-213
Author(s):  
N. M. Fujiki ◽  
K. De'Bell
Keyword(s):  
Renormalization Group ◽  
High Temperature ◽  
Square Lattice ◽  
Scaling Relations ◽  
Test Cases ◽  
Nearest Neighbour ◽  
Point Analysis ◽  
Group Methods ◽  
Ising Systems ◽  
Renormalization Group Methods

The high-temperature series renormalization group developed by Betts et al. is modified by using the decimation transformation. A conventional fixed-point analysis of the recursion relations is discussed and, in addition, an analysis based on scaling relations for correlation functions is considered. As test cases, we apply these methods to two-dimensional Ising systems with nearest neighbour interactions. The results for a triangular and a square lattice are presented.

High temperature multigraph expansions for general Ising systems

1981 ◽  
Vol 59 (1) ◽  
pp. 15-21 ◽  
Author(s):  
J. Oitmaa
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Square Lattice ◽  
Zero Field ◽  
Nearest Neighbour ◽  
Temperature Expansion ◽  
Graphical Information ◽  
Ising Systems ◽  
High Temperature Expansion ◽  
Multiple Edges

A high temperature expansion, in terms of connected graphs with single and multiple edges, is developed for general Ising systems with interactions of more than one type. The graphical information obtained is sufficient to derive 11 terms in the expansion of the high temperature zero-field susceptibility and 12 terms in the zero-field free energy for any Ising system. Series to this order are presented for the square lattice with nearest and next nearest neighbour interactions.

scholarly journals Renormalization group methods and the 2PI effective action

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
M. E. Carrington ◽  
Wei-Jie Fu ◽  
D. Pickering ◽  
J. W. Pulver
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Group Methods ◽  
Renormalization Group Methods
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