 |
|
|
|
|
1949 - 1959
Exact series expansions
For Ising ferromagnets in finite fields the challenge
became to find reliable methods of successive
approximation. Domb introduced and advocated the use of
exact series expansions of the free energy. Provided one
carefully demonstrated the regular and rapid convergence of
the solutions, it was possible to obtain fairly accurate
values for the critical exponents not only in the two-
dimensional case, but for physically meaningful three-
dimensional cases. With a center of gravity at King's
College, Domb, Sykes, Fisher, Rushbrooke, Wakefield, and
others exploited these techniques to their fullest extent,
and by the mid-1960s their work started to gain the
attention of other physicists who had originally come to
study critical phenomena from quite different perspectives.
--Karl Hall
|
| |
Exact series expansions: sources
Primary:
C. Domb, "Order-disorder statistics. II. A two-
dimensional
model," Proc. Roy. Soc. 199 A (1949): 199-221.
A smattering of other early papers in this vein:
C. Domb and M. F. Sykes, "The calculation of lattice
constants in crystal statistics," Phil Mag. 1957 2 (1957):
733-749.
Domb and Sykes, "On the susceptibility of a ferromagnet
above the Curie point," Proc. Roy. Soc. 240 A (1957):
214-228.
Domb and Sykes, "Specific heat of a ferromagnetic
substance above the Curie point," Phys. Rev. 108 (1957):
1415-1416.
M. E. Fisher and M. F. Sykes, "Excluded-volume problem
and the Ising model of ferromagnetism," Phys. Rev. 114
(1959): 45-58.
G. S. Rushbrooke and P. J. Wood, "On the
high-temperature susceptibility for the Heisenberg model,"
Proc. Phys. Soc. A 68 (1955): 1161-1169.
Secondary:
Domb 1996, 148.
Fisher 1967, 677.
Hoddeson et al., 1992, 582.
-- Karl Hall-February 22, 2002
|
|
|
