W-T identities and a candidate droplet Lagrangean for the Ising spin glass

In search for a microscopic description of “ droplet-like” properties for the Ising spin glass (single component order parameter, zero modes i.e. correlation functions vanishing at infinity) we reconsider the two-packet model of Bray and Moore, which is effectively Replica-Symmetric and enjoys zero modes but only up to one-loop. We show how an appropriate change in the limits of the basic parameters of the model (packet size and replica number) allows for a derivation of Ward–Takahashi (WT) identities, thus ensuring the existence of zero modes to all orders and opening the way for a Lagrangean formulation of a “droplet-like” field theory for the Ising spin glass.