The magnetic critical index γ is calculated by the method of real space renormalization group as a function of impurity concentration. A good agreement between the theory and the experiments is obtained.
The equivalence of the critical behavior of the d-dimensional Ising model at a finite temperature to that of a d- 1 dimensional system at zero temperature as a function of a transverse magnetic field is used to calculate the critical exponents for the three-dimensional model by applying the Niemeijer-Van Leeuwen renormalization-group method to the two-dimensional problem.
The critical relaxation of the magnetization in a two-dimensional Ising model with quenched random non-magnetic impurities has been studied by numerical simulation. A squared lattice of size 400 2 with spin concentrations p=1.0; 0.95, 0,9, 0.85, 0.8, 0.75 and 0.7 was considered. The dynamical critical exponent z was determined by the Monte Carlo method combined with the dynamical renormalization group method. The following values were received for z(p): z(1)=2.24+or-0.07, z(0.95)=2.24+or-0.06, z(0.9)=2.24+or-0.06, z(0.85)=2.38+or-0.05, z(0.8)=2.51+or-0.06, z(0.75)=2.66+or-0.07 and z(0.7)=2.88+or-0.06. A singular dynamic scaling behaviour with z=A' mod ln(p-p c ) mod +B' was found for systems with spin concentrations p<or=0.85 near the percolation threshold p c , where A'=0.56+or-0.07 and B'=1.62+or-0.07 are temperature-independent constants.
We propose a real-space renormalization-group technique to treat dynamic critical phenomena in two-dimensional Glauber-Ising models. The invariant form of the time-dependent probability distribution is found within linear response theory and an estimate of the dynamic exponent z is given.