W-T identities and a candidate "droplet" Lagrangean for the Ising Spin Glass

TL;DR

This paper develops a theoretical framework for describing droplet-like properties in the Ising spin glass using Ward-Takahashi identities, enabling a Lagrangian formulation that accounts for zero modes beyond one-loop order.

Contribution

It introduces a modified two-packet model that derives WT identities, ensuring zero modes at all orders and proposing a candidate droplet Lagrangian for the Ising spin glass.

Findings

Derivation of WT identities for the model.

Existence of zero modes to all orders.

Proposal of a droplet-like Lagrangian formulation.

Abstract

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.