  We introduce the concept of stationary metastable states (SMS's) in the
presence of another more stable state. The stationary nature allows us to study
SMS's by using a restricted partition function formalism as advocated by
Penrose and Lebowitz and requires continuing the free energy. The formalism
ensures that SMS free energy satisfies the requirement of thermodynamic
stability everywhere including T=0, but need not represent a pysically
observable metastable state over the range where the entropy under continuation
becomes negative. We consider a 1-dimensional m-component axis-spin model
involving only nearest-neighbor interactions, which is solved exactly. The
high-temperature expansion of the model representys a polymer problem in which
m acts as the activity of a loop formation. We follow deGennes and trerat m as
a real variable. A thermodynamic phase transition occurs in the model for m<1.
The analytic continuation of the high-temperature disordered phase free energy
below the transition represents the free energy of the metastable state. The
calculation shows that the notion of SMS is not necessaily a consequence of
only mean-field analysis or requires long-range interactions.
