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We study the behavior of phase transitions for the four-dimensional chargedTaub-NUT-AdS spacetime with the Newman-Unti-Tamburino (NUT) parameterinterpreted as the thermodynamic multihair in the extended thermodynamic phasespace, and mainly focus on the effects of the NUT parameter on the phasetransitions. We find that there is an upper bound on the value of the NUTparameter beyond which the corresponding physical inflection point or criticalpoint will not exist, and the thermodynamic trihair interpretation of the NUTparameter would admit a little larger upper bound than the thermodynamic bihairinterpretation. Moreover, as long as the NUT parameter is vanishingly small,the analogy to the van der Waals liquid/gas phase transition is validirrespective of the multihair characteristics of the NUT parameter. However, asthe NUT parameter increases to be comparable to the electric charge, suchanalogy to the van der Waals system will be broken, and the correspondinginflection point is not a thermodynamic critical point any more. For a largeNUT parameter, there are frequent occurrences of the zeroth order phasetransition in the case of the thermodynamic bihair interpretation, while onlythe first order phase transition happens in the case of the thermodynamictrihair interpretation.

Thermodynamical multihair and phase transitions of 4-dimensional charged Taub-NUT-AdS spacetimes