Application of Renormalization-Group Techniques to Random Magnetic Systems.

Second-order phase transitions in pure, homogeneous systems and the renormalization group framework are reviewed. Quenched random magnetic systems are introduced and momentum-space methods and position-space techniques as applied to quenched random magnets are outlined and compared. The randomly bond-dilute two-dimensional nearest-neighbor Ising model on a square lattice is studied. Calculations give both thermal and magnetic exponents associated with the percolative fixed point. Differential recursion relations yield a phase diagram which is in quantitative agreement with all known results. Curves for the specific heat, percolation probability, and magnetization are displayed. The Edwards-Anderson model of a spin glass is examined as well as the spin-1/2 Ising model with independently random nearest-neighbor interactions in dimensionalities d = 2, 3, and 4.