On a 2D lattice with m directions, all moments are forced to be zero except when m divides n .

The way the path integral for a quantum field theory works, each possible configuration of the field is in effect taken to make a contribution Exp[  s/ ℏ ] , where s is the so-called action for the field configuration (given by the integral of the Lagrangian density—essentially a modified energy density), and ℏ is a basic scale factor for quantum effects (Planck's constant divided by 2 π ).

Almost all spin configurations with e[s] > - √ 2 (where here and below all quantities are divided by the total number of spins, so that -2 ≤ e[s] ≤ 2 and -1 ≤ m[s] ≤ + 1 ) yield m[s]  0 .

In general, the period divides CarmichaelLambda[CarmichaelLambda[m]] .