which can be recognized as the kinetic energy of the field s in the sigma model. One still has two possibilities for the spin s : it is either taken from a discrete set of spins (the Potts model) or it is taken as a point on the sphere S n − − 1 ; that is, s is a continuously-valued vector of unit length. In the later case, this is referred to as the O ( n ) non-linear sigma model, as the rotation group O ( n ) is group of isometries of S n − − 1 , and obviously, S n − − 1 isn't "flat", i.e. isn't a linear field.