On the Orders of Lineal Phase Transitions

“Lineal” is a type of relationship between ferroic phases derived from one prototypic phase, as was explained in previous papers. A lineal transition of rank difference 1, i.e., the transition between two lineal phases whose ranks differ by 1 can be second order A lineal transition of rank difference>1 (let the two relevant phases be called α and β) cannot be second order, if in the homophone sequence there is a possible phase that is lineal both to phase α and to phase β and whose rank is intermediate between the ranks of phases α and β On the other hand, if there is no intermediate-rank lineal phase, the lineal transition of rank difference >1–despite being of rank difference >1–can be second order. Detailed elucidations of these are made with two simple examples of homophone sequences.