  We show how to obtain all the models of the continuous description of
membranes by constructing the appropriate non-linear realizations of the
Euclidean symmetries of the embedding. The procedure has the advantage of
giving a unified formalism with which the models are generated and highlights
the relevant order parameters in each phase. We use our findings to investigate
a fluid description of both tethered and hexatic membranes, showing that both
the melting and the loss of local order induce long range interactions in the
high temperature fluid phase. The results can be used to understand the
appearance of intrinsic ripples in crystalline membranes in a thermal bath.
