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 d̄=[d+1ν(d̄)]2 for the thermal exponents if α(d̄)<~0. The consequences for Ising systems are particularly reliable at the upper and lower critical dimensions (du.c.d.=6 and dl.c.d.=2, respectively) as well as at $d=3$ where α=0 (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).