  The existence and limits of metastable droplets have been calculated using
finite-system renormalization-group theory, for q-state Potts models in spatial
dimension d=3. The dependence of the droplet critical sizes on magnetic field,
temperature, and number of Potts states q has been calculated. The same method
has also been used for the calculation of hysteresis loops across first-order
phase transitions in these systems. The hysteresis loop sizes and shapes have
been deduced as a function of magnetic field, temperature, and number of Potts
states q. The uneven appearance of asymmetry in the hysteresis loop branches
has been noted. The method can be extended to criticality and phase transitions
in metastable phases, such as in surface-adsorbed systems and water.
