scholarly journals Low-temperature series for Ising model by finite-lattice method

1995 ◽  
Vol 42 (1-3) ◽  
pp. 740-742
Author(s):  
H. Arisue ◽  
K. Tabata
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Finite Lattice ◽  
Temperature Series ◽  
Lattice Method

scholarly journals Some Algebraic Techniques for obtaining Low-temperature Series Expansions

1978 ◽  
Vol 31 (6) ◽  
pp. 515 ◽  
Author(s):  
IG Enting
Keyword(s):  
Low Temperature ◽  
Statistical Mechanics ◽  
Series Expansion ◽  
General Result ◽  
Generating Functions ◽  
Finite Lattice ◽  
Lattice Models ◽  
Temperature Series ◽  
Series Expansions ◽  
Lattice Method

It is shown that low-temperature series expansions for lattice models in statistical mechanics can be obtained from a consideration of only connected strong subgraphs of the lattice. This general result is used as the basis of a linked-cluster form of the method of partial generating functions and also as the basis for extending the finite lattice method of series expansion to low-temperature series.

Low-temperature series for the Ising model

1970 ◽  
Vol 3 (8) ◽  
pp. 1652-1660 ◽  
Author(s):  
C Domb ◽  
A J Guttmann
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Series

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4911-4917
Author(s):  
YEE MOU KAO ◽  
MALL CHEN ◽  
KEH YING LIN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Spontaneous Magnetization ◽  
Temperature Series ◽  
Square Lattice ◽  
Series Expansions ◽  
Zero Field ◽  
Ferromagnetic Ising Model ◽  
Neighbour Interaction

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

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