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 ${\ensuremath{\alpha}}_{\mathrm{pure}<0}$, independent of the value of the concentration.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 ${\ensuremath{\alpha}}_{\mathrm{pure}<0}$, independent of the value of the concentration.

Physical review. B, Condensed matterAug 1, 198920 citations

Behaviour of systems near the polycritical point

A.Z. Patashinsky, B.I. Shumilo

Physics Letters AApr 1, 19770 citations

Scaling function near a fluctuation-induced tricritical point

M. L. Lyra, Mauricio D. Coutinho-Filho

Physics Letters AMay 1, 19921 citation

Effect of elastic deformations on the critical behavior of disordered systems with long-range interactions

С. В. Белим

A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter. Renormalization-group equations are analyzed in the two-loop approximation by using the Padé-Borel summation technique. The fixed points corresponding to critical and tricritical behavior of the systems are determined. Elastic deformations are shown to changes in critical and tricritical behavior of disordered compressible systems with long-range interactions. The critical exponents characterizing a system in the critical and tricritical regions are determined.A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter. Renormalization-group equations are analyzed in the two-loop approximation by using the Padé-Borel summation technique. The fixed points corresponding to critical and tricritical behavior of the systems are determined. Elastic deformations are shown to changes in critical and tricritical behavior of disordered compressible systems with long-range interactions. The critical exponents characterizing a system in the critical and tricritical regions are determined.

arXiv:cond-mat/0502098Journal of Experimental and Theoretical PhysicsFeb 1, 20043 citations

Equations of State for Tricritical Points

David R. Nelson, Joseph Rudnick

Renormalization-group recursion relations are used to calculate to order $\ensuremath{\epsilon}=4\ensuremath{-}d$ the free-energy, ordering-susceptibility, and magnetization-crossover scaling functions for tricritical points in isotropic $n$ -vector models. The equations of state describe critical and tricritical behavior in both ordered and disordered phases.Renormalization-group recursion relations are used to calculate to order $\ensuremath{\epsilon}=4\ensuremath{-}d$ the free-energy, ordering-susceptibility, and magnetization-crossover scaling functions for tricritical points in isotropic $n$-vector models. The equations of state describe critical and tricritical behavior in both ordered and disordered phases.

Physical Review LettersJul 21, 1975105 citations

{T}_{c}

) is not changed by dilution if the critical exponent of the specific heat of the pure system ${\ensuremath{\alpha}}_{\mathrm{pure}<0}$, independent of the value of the concentration.

n

-vector models. The equations of state describe critical and tricritical behavior in both ordered and disordered phases.