Nonperturbative Critical Behavior of Random-Field Systems

The thermal critical properties of random-field systems in the observable, linear, local-response regime are considered. A consistent nonperturbative approach yields an effective reduced dimension $\overline{d}=\frac{[d+\frac{1}{\nu \left(\overline{d}\right)}]}{2}$ for the thermal exponents if $\alpha \left(\overline{d}\right)<~0$. The consequences for Ising systems are particularly reliable at the upper and lower critical dimensions ($d_{\mathrm{u}.\mathrm{c}.\mathrm{d}.\mathrm{}}=6\mathrm{}$ and $d_{\mathrm{l}.\mathrm{c}.\mathrm{d}.\mathrm{}}=2\mathrm{}$, respectively) as well as at $d=3\mathrm{}$ where $\alpha =0\mathrm{}$ (logarithmic divergence). The results are in agreement with measurements on random antiferromagnets of the specific heat (by linear birefringence) and the correlation length (by neutron scattering).