The dynamic critical exponents for percolating ferromagnets and antiferromagnets

Abstract

We have introduced the new dynamic critical exponents – the fractal dimensions z s=2+( μ− g)/ ν and z v=[2+(2 μ− g−2 β)/ ν] for the spin-stiffness coefficient of percolation ferromagnet and antiferromagnet, respectively, and associated them with the static critical exponents ν and β. We have obtained two different universality classes for dynamical critical phenomena, that depend on scalar (for conductivity with the critical exponent μ=1.92) and vector (for the Hall coefficient with the critical exponent g=0.6) nature of forces. Diffusion, stiffness coefficients, elastic moduli and ferromagnets and antiferromagnets belong to both of them. These results allow us to obtain new formulae for vibration density of states for scalar and vector elasticity and for the spin-stiffness coefficient of percolating magnets and to compare our formulae with available experimental data at the critical point.