Statistics of the simple cubic lattice. II

Abstract

Experimentally it is found for a ferromagnetic substance that the spontaneous magnetization decreases as the temperature increases. At a certain temperature called the Curie point, the magnetization disappears (or substantially disappears) and remains zero for higher temperatures. Associated with these magnetic properties is an anomaly in the specific heat. This quantity is greater than that which would be calculated theoretically for the material were it non-magnetic and becomes large when the temperature approaches the Curie point from below. Just above the Curie point there is a sharp but continuous decrease in the specific heat and the system is said to show critical behaviour. We shall examine the Ising model of the ferromagnet with a simple cubic lattice structure, determine the specific heat anomaly and the corresponding energy excess due to magnetism, and also see how the critical behaviour of the model compares with that actually observed.