Complete listing of order parameters for a crystalline phase transition: A solution to the generalized inverse Landau problem

For a given group-subgroup transition, the complete set of order parameters, primary and secondary, describe the distortions that accompany this transition. The task of obtaining all order-parametric distortions for a group-subgroup pair is a long standing problem. An algorithm is presented here which obtains the irreducible representations and order parameter directions for an arbitrary transition. Examples are given for a variety of phase transitions showing the application and utility of the procedure. It is shown that a unique selection of primary order parameters is not always possible.