The name of this model comes from its rotational symmetry. Consider the low temperature behavior of this system and assume that there exists a spontaneously broken symmetry, that is a phase where all spins point in the same direction, e.g. along the x -axis. Then the O (n) rotational symmetry of the system is spontaneously broken, or rather reduced to the O (n − 1) symmetry under rotations around this direction. We can parametrize the field in terms of independent fluctuations { σ σ α α : α α = 1 , … … , n − − 1 } around this direction as follows: