  We briefly introduce hysteresis in spatially extended systems and the dynamic
phase transition observed as the frequency of the oscillating field increases
beyond a critical value. Hysteresis and the decay of metastable phases are
closely related phenomena, and a dynamic phase transition can occur only for
field amplitudes, temperatures, and system sizes at which the metastable phase
decays through nucleation and growth of many droplets. We present preliminary
results from extensive Monte Carlo simulations of a two-dimensional kinetic
Ising model in a square-wave oscillating field and estimate critical exponents
by finite-size scaling techniques adapted from equilibrium critical phenomena.
The estimates are consistent with the universality class of the two-dimensional
equilibrium Ising model and inconsistent with two-dimensional random
percolation. However, we are not aware of any theoretical arguments indicating
why this should be so. Thus, the question of the universality class of this
nonequilibrium critical phenomenon remains open.
