  Supersymmetric quantum mechanics is well known to provide, together with the
so-called shape invariance condition, an elegant method to solve the eigenvalue
problem of some one-dimensional potentials by simple algebraic manipulations.
In the present paper, this method is used in statistical physics. We consider
the local critical behaviour of inhomogeneous Ising models and determine the
complete set of anomalous dimensions from the spectrum of the corresponding
transfer matrix in the strip geometry. For smoothly varying perturbations, the
eigenvalue problem of the transfer matrix indeed takes the form of a
Schr\"odinger equation, and the corresponding potential furthermore exhibits
the shape invariance property for some known extended defects. In these cases,
the complete spectrum is derived by the methods of supersymmetric quantum
mechanics.
