Random-field critical behavior of ad=3Ising system

Optical birefringence studies of the randomly diluted, $d=3\mathrm{}$ Ising antiferromagnet ${\mathrm{Fe}}_{0.6}$ ${\mathrm{Zn}}_{0.4}$ ${\mathrm{F}}_2$ reveal that the magnetic specific heat exhibits a symmetric logarithmic singularity, consistent with an effective dimensionality $\overline{d}\simeq 2$, in small magnetic fields $H$ applied parallel to the unique axis. The nature and the sharpness of the phase transition for $H\le 20$ kOe and reduced temperature $5\times {10}^{-4\mathrm{}}\le t\le {10}^{-1\mathrm{}}$ suggest that the lower critical dimensionality $d_l<3\mathrm{}$. Both of these results are inconsistent with the predicted mapping $\overline{d}=d-2\mathrm{}$, for the random-field problem, obtained from perturbation theory. The observed crossover exponent $\phi =1.40\mathrm{}\pm 0.05$ agrees with both the measured and predicted random-exchange susceptibility exponent $\gamma$ as is to be expected. The observed amplitude of the shift in $T_c$ with $H$ agrees with a new theory of random-field effects in diluted antiferromagnets.