Measures of Spin Ordering in the Potts Model with a Generalized External Magnetic Field

We formulate measures of spin ordering in the $q$-state ferromagnetic Potts model in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s=\{1,\mathrm{.}\mathrm{.}\mathrm{.},s\}$ of the total set of $q$ values. The results are contrasted with the corresponding measures of spin ordering in the case of a conventional external magnetic field that favors or disfavors a single spin value out of total set of $q$ values. Some illustrative calculations are included.