In many solids the intermolecular forces are sufficiently short ranged so that practically the entire potential energy of the system results from interactions between nearest neighbors. The thermodynamic properties of a solid with respect to a given coordinate, α, (for example, in a ferromagnetic system α might represent the excess unpaired electron spin at a given lattice point; or in a substitutional binary alloy α might denote which of the two possible kinds of atoms are at a given lattice point) can be found from the factor of the partition function which averages over all possible configurations of α at all lattice points.Here the evaluation of such a factor of the partition function is reduced to the calculation of the largest characteristic value of a linear homogeneous operator equation involving the potential energy between two adjacent layers of lattice points in the solid. By assuming that all possible configurations of a layer are equally probable, a lower bound for the partition function for ...
[1]
J. Kirkwood.
On Phase Changes in Crystals Arising from Hindered Molecular Rotation
,
1940
.
[2]
R. Oldenburger,et al.
Infinite powers of matrices and characteristic roots
,
1940
.
[3]
W. Shockley,et al.
Order-Disorder Transformations in Alloys
,
1938
.
[4]
F. Bitter.
Introduction to ferromagnetism
,
1937
.
[5]
M. Blackman.
Contributions to the theory of the specific heat of crystals I—Lattice theory and continuum theory
,
1935
.
[6]
K. Herzfeld,et al.
On the States of Aggregation
,
1934
.
[7]
J. V. Vleck,et al.
The theory of electric and magnetic susceptibilities
,
1934,
The Mathematical Gazette.
[8]
E. Ising.
Beitrag zur Theorie des Ferromagnetismus
,
1925
.