Critical phenomena of random spin systems: Second order ϵ-expansion

Abstract

The critical behaviour of quenched random spin systems is studied within a renormalization group approach. The critical exponents for the broken scaling laws are calculated in second order in ε =4− d. It can be shown that in the region of small concentration of the magnetic atoms α → − 1, β → 0.5, γ → 2 and δ → 5. These exponents turn out to be independent of the order parameter dimension n. The exponents of the non-leading singularities for small ε are in this order of ε no longer negligible in three dimensions ( ε = 1) and the related singularities may become dominant, if n is small enough (Ising magnet!).