https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
[0] https://onlinelibrary.wiley.com/doi/epdf/10.1002/anie.201302...
In gold it changes the color, in Mercury it changes freezing temperature.
Gallium has a low melting point 29.76C but that is due to unique chemical bonding.
"relativistic contraction" (shrinking of s and p orbitals) and "relativistic expansion" (destabilization of d and f orbitals) causes many observed phenomena.
Relativistic contraction of the 6s orbital and expansion of the 5d orbital lower the energy required to excite electrons. Consequently, gold absorbs blue light.
Strong relativistic contraction of the outer 6s electrons leaves them tightly bound and unavailable for metallic bonding. This results in incredibly weak atomic interactions, thus mercury a liquid at room temperature.
Lead also has 6s, which is what makes lead acid batteries work as well as they do.
So while the observed effects change, there are relativity effects with several nearby neighbors.
And here come the relativistic effects, which essentially scale with nuclear charge of the nucleus come to play and they are significantly stronger for Hg than Cd. If I remember correctly (although I read about it a long time ago so I may be a bit rusty) these strong relativistic effects cause something called "relativistic contraction of the 6s orbital" which results in the electrons on this orbital being more strongly bound than they would be, if there would be no relativistic effects (which can be theoretically compared by setting c -> infinity in the equations used to solve electronic structure theory). AFAIR Copernicium should also be liquid in room temperature for similar reasons, but since it is not very long lived and it is difficult to produce testing this will likely be very hard if not impossible to check (though if I remember correctly there was something called "relativistic maximum" which happens in the 6th and not 7th row of periodic table for some reason, so it should be higher than for mercury; though I can't remember the details why this is so).
Of course this is a bit simplified picture and there are surely more details regarding how exactly relativistic effects influence the energies and consequently how this influences the melting temperature of mercury (I suppose they are in the Calvo, Pahl, Wormit and Schwerdtfeger paper linked earlier in this thread), but I think the combination of the electron configuration and strong relativistic effects explain why other neighbors are not liquid.
Without relativistic effects a lead acid battery would put out about .2V rather than 2V.
More details at: https://arxiv.org/abs/1008.4872