Random-field-induced destruction of the phase transition of a diluted two-dimensional Ising antiferromagnet: ${\mathrm{Rb}}_2$${\mathrm{Co}}_{0.85}$${\mathrm{Mg}}_{0.15}$${\mathrm{F}}_4$

Optical birefringence has been used to study the effects of a uniform field $H$ on the magnetic specific heat $C_m$ near the phase transition of a randomly diluted, two-dimensional (2D) Ising antiferromagnet, ${\mathrm{Rb}}_2$ ${\mathrm{Co}}_{0.85}$ ${\mathrm{Mg}}_{0.15}$ ${\mathrm{F}}_4$. For $H=0\mathrm{}$, a well-defined transition is observed with a symmetric logarithmic divergence in $C_m$, corresponding to the critical exponent $\alpha =0\mathrm{}$, as is predicted for the 2D Ising random-exchange case. With $\overrightarrow{\mathrm{H}}$ applied parallel to the $c$ axis, a systematic rounding of the peak in $C_m$ occurs which increases with increasing $H$. This demonstrates that induced random fields destroy the phase transition and that the lower critical dimensionality for the random-field problem $d_l\ge 2$. No rounding is found with $\overrightarrow{\mathrm{H}}\perp c$, as expected. The peak in $C_m$ with $\overrightarrow{\mathrm{H}}\parallel c$ exhibits a decrease in amplitude, which varies as $\ln H$. This behavior, together with the ln $\left|t\right|$ dependence of $C_m$ at $H=0\mathrm{}$, was used to determine the crossover exponent $\phi =1.58\mathrm{}\pm 0.22$. This value is in essential agreement with the exactly known critical exponent of the staggered susceptibility $\gamma$ for the 2D Ising problem, namely $\gamma =\frac{7}{4}$, as predicted theoretically. By suitable rescaling, the rounded peaks found for different values of $H$ may all be collapsed to a single curve in the critical region, in accord with renormalization-group scaling relations. The shift and rounding (and hence the peak amplitude) are in quantitative agreement with the site-diluted, random-field predictions.