Thermodynamics of the(1,12)ferrimagnet in finite magnetic fields

We investigate the specific heat and magnetization of a ferrimagnet with $gS=1\mathrm{}$ and $S=\frac{1}{2}$ spins in a finite magnetic field using the transfer matrix density matrix renormalization group down to $T=0.025J.\mathrm{}$ Ferromagnetic gapless and antiferromagnetic gapped excitations for $H=0\mathrm{}$ lead to rich thermodynamics for $H>~0.$ While the specific heat is characterized by a generic double peak structure, magnetization reveals two critical fields, $H_{c1\mathrm{}}=1.76\mathrm{}\left(1\right)J$ and $H_{c2\mathrm{}}=3.00\mathrm{}\left(1\right)J$ with square-root behavior in the $T=0\mathrm{}$ magnetization. Simple analytical arguments allow us to understand these experimentally accessible findings.