No Phase Transition in a Magnetic Field in the Ising Spin Glass F${\mathrm{e}}_{0.5}$M${\mathrm{n}}_{0.5}$Ti${\mathrm{O}}_3$

The dynamic scaling behavior of the Ising spin glass F${\mathrm{e}}_{0.5}$M${\mathrm{n}}_{0.5}$Ti${\mathrm{O}}_3$ in superimposed dc magnetic fields has been studied. The dynamic freezing temperatures $T_f\left(\omega ,H\right)$ were determined as a function of field $0\le H\le 3.1$ T and frequency $0.017\le \omega /2\mathrm{}\pi \le 5100$ Hz. The in-field scaling behavior is strikingly different from the zero-field behavior and is well described by activated dynamics and a correlation length that depends on field as $\xi \propto H^{-{\nu }_H}$. The results are in agreement with the droplet model predictions and strongly suggest that there is no phase transition in a magnetic field in 3D Ising spin glasses.