Numerical studies of the field dependence of the magnetic specific heat of ${\mathrm{Eu}}_{0.25}$ ${\mathrm{Sr}}_{0.75}$S and ${\mathrm{Eu}}_{0.54}$ ${\mathrm{Sr}}_{0.46}$S

We use numerical simulation methods to determine the magnetic specific heat of ${\mathrm{Eu}}_{0.25}$ ${\mathrm{Sr}}_{0.75}$ and ${\mathrm{Eu}}_{0.54}$ ${\mathrm{Sr}}_{0.46}$S as a function of field and temperature over the range $0.1\le T\le 3$ K and $0\le B\le 6$ T. For $x=0.25\mathrm{}$ agreement with experiment is obtained at 1 K for $B>\mathrm{}1\mathrm{}$ T; for $x=0.54\mathrm{}$ agreement is obtained at 1 K in zero field and for fields above 1 T. Possible explanations for the discrepancy at low fields are advanced. The calculations are carried out in the independent-boson approximation so that as a by-product we obtain data on the field dependence of the distribution of magnon modes. The effect of fields above 3-4 T is to introduce a uniform shift in the magnon energies. At low fields the effect is more complicated as it involves a change in the relative distribution of the modes as well as a shift in their energies. Since the calculations involve no adjustable parameters, they provide additional confirmation of earlier results that magnons make the dominant contribution to the specific heat of Heisenberg spin glasses at low temperatures.