The propagation of order in co-operative phenomena

Abstract

A new attack is made on the order-disorder problem. On the basis of Bethe's hypothesis of nearest neighbour action an approximate relation is derived connecting the probabilities at adjacent lattice sites. This has the form of a non-linear finite difference equation, which proves to be a powerful mathematical tool, governing the properties above as well as below the critical transition temperature. The resulting critical values are practically equal to those of Bethe. At variance with all former theories, however, the specific heat is found to show no abrupt change at the transition point. The theory is also applied to AB superstructures with face-centered lattice. A finite heat of transition is found in this case, together with a thermodynamical irreversibility which may account for the observed hysteresis effects.