  A central qubit coupled to an Ising ring of $N$ qubits, operating close to a
critical point is investigated as a potential precision quantum magnetometer
for estimating an applied transverse magnetic field. We compute the Quantum
Fisher information for the central, probe qubit with the Ising chain
initialized in its ground state or in a thermal state. The non-unitary
evolution of the central qubit due to its interaction with the surrounding
Ising ring enhances the accuracy of the magnetic field measurement. Near the
critical point of the ring, Heisenberg-like scaling of the precision in
estimating the magnetic field is obtained when the ring is initialized in its
ground state. However, for finite temperatures, the Heisenberg scaling is
limited to lower ranges of $N$ values.
