Phase diagram for a random mixture of competing Ising anisotropies

We study a ferromagnetic system in which each bond can be either of the Ising type (${\sigma }^Z{\sigma }^Z$) or of anisotropic Heisenberg (Ising ${\sigma }^Z{\sigma }^Z$-like) type, at random with respective concentrations ($1-p$) and $p$. A global phase diagram in the temperature-anisotropy-concentration space is obtained within the Migdal-Kadanoff approximation. For the paramagnetically ordered transitions, our results for the critical temperature as a function of $p$ agree very well with those obtained experimentally for ${\mathrm{Fe}}_{1-p}{\mathrm{Co}}_p{\mathrm{Cl}}_2· {2\mathrm{H}}_2\mathrm{O}$.