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Supersymmetric quantum mechanics is well known to provide, together with theso-called shape invariance condition, an elegant method to solve the eigenvalueproblem of some one-dimensional potentials by simple algebraic manipulations.In the present paper, this method is used in statistical physics. We considerthe local critical behaviour of inhomogeneous Ising models and determine thecomplete set of anomalous dimensions from the spectrum of the correspondingtransfer matrix in the strip geometry. For smoothly varying perturbations, theeigenvalue problem of the transfer matrix indeed takes the form of aSchr\"odinger equation, and the corresponding potential furthermore exhibitsthe shape invariance property for some known extended defects. In these cases,the complete spectrum is derived by the methods of supersymmetric quantummechanics.Comment: Tex,iopppt.tex,13 pages,4 figure

Realization of supersymmetric quantum mechanics in inhomogeneous Ising models