What is the minimum thickness of a wall in stone masonry?

It is generally considered to be 6″. You can get thinner but stone size, shape orientation, and reinforcement quickly become predominant issues.

In other words, the wall starts behaving more like concrete bellow 6″ in thickness and like a shell structure below 4″ in thickness.

Keep in mind when I say they behave in a certain way, I’m saying you need to adjust your materials to fall in line with walls of that thickness.