Assuming you meant 4.579 mmHg, you can first convert to atm by dividing your given pressure by 760 (1 atm = 760 mmHg). You end up with 0.006 atm for pressure. This is a significant number because at 0.01 degree C, this is the triple point of water.
So below this pressure only two phases can exist (excluding the triple point): solid and gaseous water. However, in order to truly specify what phase can exist at a given pressure, you would also need to specify the temperature as well. At the triple point, all three phases of water exist simultaneously, they are essentially in equilibrium with one another. As you increase T at this pressure, only the gas phase will exist.
Check our this phase diagram so you can visualize what we are talking about.
https://courses.lumenlearning.com/cheminter/chapter/phase-diagram-for-water/