  We examine the thermodynamics of Euclidean dyonic Taub-NUT/Bolt-AdS4 black
holes for a variety of horizon geometries to understand how gauge field
regularity conditions influence the thermodynamic relations. We find several
distinct features that distinguish the NUT-charged case from its dyonic
Reissner-Nordstrom counterpart. For the NUT solution, the gauge field vanishes
at the horizon and so regularity is ensured. For the Bolt solution we find that
the norm of the gauge field is required to vanish at the horizon in order to
satisfy both regularity and the first law of thermodynamics. This regularity
condition yields a constraint on the electric and magnetic charges and so
reduces cohomogeneity of the system; for spherical horizons, the regularity
condition removing the Misner string singularity further reduces cohomogeneity,
We observe that bolt solutions with increasing electric charge have positive
heat capacity, but upon turning on the magnetic charge to make the solution
dyonic, we find that the properties of the uncharged one are retained, having
both positive and negative heat capacity. We also study the extremal Bolt
solution, finding that Misner string disappears at the horizon in the zero
temperature limit. We find that the extremal solution has
finite-temperature-like behaviour, with the electric potential playing a role
similar to temperature.
