The crystal statistics of the diamond lattice

Abstract

The crystal statistics of the Ising Model Diamond Lattice are investigated by series methods. Unlike most three-dimensional lattices this lattice has low temperature expansions that converge up to the Curie point and this enables the specific heat and spontaneous magnetisation to be estimated within narrow limits. The Curie temperature is found to be kTc/qJ − 0.6760 ± 0.0001, the critical energy Ec/kTc = 0.418 and the critical entropy Se/k = 0.511. The specific heat is found to have a logarithmic singularity as the Curie point is approached from below and the spontaneous magnetisation vanishes as (Tc − T)h where h = 0.312 ± 0.002 and it is conjectured that h is exactly 5/16. The attrition parameter for the excluded volume problem is found to be μ = 2.878 ± 0.002.