To find the behavior of fluctuations, rescale the field to fix the gradient term. Then the length scaling dimension of the field is 1 − d /2. Now the field has constant quadratic spatial fluctuations at all temperatures. The scale dimension of the H term is 2, while the scale dimension of the H term is 4 − d. For d < 4, the H term has positive scale dimension. In dimensions higher than 4 it has negative scale dimensions.