What is the Latin root for physician?

The root for 'physician' is ultimately Greek, although we get the Word via Latin.

The Middle LidDELL dictionary definition of the Greek Word φυσις (phusis) is 'The nature of a person or a thing, i.e the natural form or constitution...'

One who concerned themselves with this was a φυσικος (phusikos).

Latin used this Word too, but transliterated it into their alphabet: 'physicus' and hence we get our Word 'physician' - lit. 'one who concerns themselves with the nature of things'.

Latin more commonly used the Word 'medicus' to mean 'physician' as we use the Word today.