  Two- and three-dimensional Kitaev magnets are prototypical frustrated quantum
spin systems, in which the original spin degrees of freedom fractionalize into
Majorana fermions and a $\mathbb{Z}_2$ gauge field -- a purely local phenomenon
that reveals itself as a thermodynamic crossover at a temperature scale set by
the strength of the bond-directional interactions. For conventional Kitaev
magnets, the low-temperature thermodynamics reveals a second transition at
which the $\mathbb{Z}_2$ gauge field orders and the system enters a spin liquid
ground state. Here we discuss an explicit example that goes beyond this
paradigmatic scenario -- the $\mathbb{Z}_2$ gauge field is found to be subject
to geometric frustration, the thermal ordering transition is suppressed, and an
extensive residual entropy arises. Deep in the quantum regime, at temperatures
of the order of one per mil of the interaction strength, the degeneracy in the
gauge sector is lifted by a subtle interplay between the gauge field and the
Majorana fermions, resulting in the formation of a Majorana metal. We discuss
the thermodynamic signatures of this physics obtained from large-scale,
sign-free quantum Monte Carlo simulations.
