Thermodynamic behavior of quenched random magnets from a position-space renormalization group

The inhomogeneous generalization of the Migdal-Kadanoff approximate recursion relations is used to study the properties of Ising magnets with spatially random (quenched) couplings. Simple calculations in two dimensions produce qualitatively reasonable phase diagrams and critical exponents for both a dilution problem (nearest-neighbor couplings 0 and J) and a spin-glass system (nearest-neighbor coupling +J and −J. Other related work is briefly reviewed.