scholarly journals Specific-heat exponent for the three-dimensional Ising model from a 24th-order high-temperature series

1994 ◽  
Vol 49 (18) ◽  
pp. 12909-12914 ◽  
Author(s):  
Gyan Bhanot ◽  
Michael Creutz ◽  
Uwe Glässner ◽  
Klaus Schilling
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Three Dimensional ◽  
Temperature Series

High-temperature specific heat series of the Ising model on the crystobalite lattice

1970 ◽  
Vol 48 (3) ◽  
pp. 307-312 ◽  
Author(s):  
R. W. Gibberd
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Partition Function ◽  
Specific Heat ◽  
Temperature Series ◽  
Padé Approximant ◽  
Reliable Estimate ◽  
Pade Approximant

Betts and Ditzian have recently published the first 11 coefficients of the exact high-temperature series for the specific heat of the spin 1/2 Ising model on a crystobalite lattice. In this paper the exact coefficients for the next 8 terms are derived by making use of an approximate transformation between the Ising partition function of the crystobalite and diamond lattices. The series is analyzed by using the ratio and Padé approximant methods, but a reliable estimate for α has not been obtained.

High and Low Temperature Series Estimates for the Critical Temperature of the 3D Ising Model

1998 ◽  
Vol 09 (01) ◽  
pp. 195-209 ◽  
Author(s):  
Zaher Salman ◽  
Joan Adler
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Three Dimensional ◽  
Temperature Series ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Error Bars ◽  
Temperature Side ◽  
3D Ising Model

We have analyzed low and high temperature series expansions for the three-dimensional Ising model on the simple cubic lattice. Our analysis of Butera and Comi's new 21-term high temperature series yields [Formula: see text] and from the 32-term low temperature series of Vohwinkel we find Kc=0.22167±0.00002, consistent with the high temperature series but with larger error bars. We discuss the reasons for the larger error bars on the low temperature side and compare these values with estimates from other series analyses and from simulations.

Extended high temperature low field expansions for the Ising model

1979 ◽  
Vol 57 (8) ◽  
pp. 1239-1245 ◽  
Author(s):  
S. McKenzie
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Ising Model ◽  
Three Dimensional ◽  
Low Field ◽  
Hypercubic Lattice

High temperature low field expansions are derived from the free energy of the Ising model for several two- and three-dimensional lattices. These represent a considerable advance on earlier work. Expansions for the four-dimensional hypercubic lattice are also presented.

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