The spinodal is the boundary where a metastable phase loses local stability. In a mean-field free-energy description the relevant curvature vanishes there, separating local minima from unstable configurations.
A spinodal point is the limit of local metastability of a phase. At a mean-field spinodal, a local minimum merges with a neighboring maximum and the corresponding second derivative of the free energy vanishes.
For the Landau free energy with and , stationary branches satisfy . Their local stability requires . At a spinodal point, and , giving the displayed field magnitude. Following local minima without nucleation produces a hysteresis loop switching at these limits. Equilibrium instead switches between the two global minima at .
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The term "spinodal" is primarily used in the context of thermodynamics, specifically in phase separation processes in materials science and physical chemistry. It refers to a specific type of phase transition that occurs when a mixture is unstable and can separate into two or more distinct phases. In a broader sense, spinodal decomposition is a mechanism that describes how a homogeneous mixture becomes unstable. The spinodal curve defines the limits within which phase separation can occur spontaneously, even without nucleation.