What is the state of water at exactly 0°C?

Theoretically speaking, what is the state of water at bang on 0°C - not any lower or higher?

Any lower would make it a solid whereas any higher would make it a liquid. But what about bang on 0°C?

Thanks in advance

Edit: I understand that other factors are involved, such as pressure and temperature which would shift the equilibrium, but in a 'theoretical perspective', what would occur - assuming that all of the particles are at exactly the same temperature with the same kinetic energy?

Answer

At the transition point between two phases, both states are thermodynamically (meta)stable. The actual composition, however, is kinetically determined and will depend on the history of how you got to 0$^\circ$C and how long you wait.

For instance, if pure water (no impurities and in a container that does not induce heterogeneous nucleation) is cooled slowly enough then it will remain liquid at 0$^\circ$C for a very long time (until a critical ice nucleus spontaneously forms). In fact, it can reach as low as -10$^\circ$C without freezing (i.e. it becomes supercooled).

If you had an infinitely large block of ice (i.e. no surfaces) and warmed it up to 0$^\circ$C then it would also remain solid for a very long time (again, until a spontaneous critical nucleation event). With surfaces, however, the surfaces will melt and the system will slowly move towards a state consisting of both liquid and ice.