  Critical behaviour in phase transitions is a resource for enhanced precision
metrology. The reason is that the function, known as Fisher information, is
superextensive at critical points, and, at the same time, quantifies
performances of metrological protocols. Therefore, preparing metrological
probes at phase transitions provides enhanced precision in measuring the
transition control parameter. We focus on the Lipkin-Meshkov-Glick model that
exhibits excited state quantum phase transitions at different magnetic fields.
Resting on the model spectral properties, we show broad peaks of the Fisher
information, and propose efficient schemes for precision magnetometry. The
Lipkin-Meshkov-Glick model was first introduced for superconductivity and for
nuclear systems, and recently realised in several condensed matter platforms.
The above metrological schemes can be also exploited to measure microscopic
properties of systems able to simulate the Lipkin-Meshkov-Glick model.
