Crossover theory for disordered ferromagnets

Abstract

We show that the critical behavior of disordered ferromagnets can be understood in terms of an effective, translational invariant Hamiltonian with renormalized coupling parameters which exhibit a tricritical as well as a critical point. The stable critical fixed point describes the critical behavior of weakly disordered systems, whereas the tricritical fixed point is responsible for the critical behavior of strongly disordered systems at least in the experimentally accessible range of temperature. This necessitates a crossover theory to describe the crossover between these two fixed points and to calculate critical properties as a function of concentration and temperature. In this paper we study the symmetric phase. Susceptibility and specific heat are calculated in scaling form using nonlinear scaling fields to verify that disordered ferromagnets exhibit universal critical behavior. The corresponding effective exponents exhibit nonmonotonous concentration- and temperature-dependent behavior. According to our theory, Fisher-renormalized tricritical behavior dominates in the experimentally accessible temperature range which leads to extreme values of the effective exponents ${\ensuremath{\gamma}}_{\mathrm{eff}}$=2 and ${\ensuremath{\alpha}}_{\mathrm{eff}}$=-1 in the limit of strong dilution. However, in accord with the Harris criterion we verify that the asymptotic behavior (T\ensuremath{\rightarrow}${T}_{c}$) is not changed by dilution if the critical exponent of the specific heat of the pure system ${\ensuremath{\alpha}}_{\mathrm{pure}l0}$, independent of the value of the concentration.