  The thermal phase transitions of a spin-1/2 Ising-Heisenberg model on the
diamond-decorated square lattice in a magnetic field are investigated using a
decoration-iteration transformation and classical Monte Carlo simulations. A
generalized decoration-iteration transformation maps this model exactly onto an
effective classical Ising model on the square lattice with
temperature-dependent effective nearest-neighbor interactions and magnetic
field strength. The effective field vanishes along a ground-state phase
boundary of the original model, separating a ferrimagnetic and a quantum
monomer-dimer phase. At finite temperatures this phase boundary gives rise to
an exactly solvable surface of discontinuous (first-order) phase transitions,
which terminates in a line of Ising critical points. The existence of
discontinuous reentrant phase transitions within a narrow parameter regime is
reported and explained in terms of the low-energy excitations from both phases.
These exact results, obtained from the mapping to the zero-field effective
Ising model are corroborated by classical Monte Carlo simulations of the
effective model.
