Crises as instabilities in an effective theory model of market response

We show that effective Lagrangian modeling of fluctuations in a market network plus dissipation explains a phenomenological model previously introduced by us. Our results suggested that the model identified the time-line of the 2009-2011 Eurozone crisis correctly. Assuming sparsity of connections -- which holds for Eurozone crisis -- we derive analytically derive the phases and where the phase transition happens. We show that this model has three distinct phases that can broadly be categorized as ``stable'' and ``unstable''. Based on the interpretation of our behavioral parameters, the stable phase describes periods where investors and traders have confidence in the market (e.g. predict that the market rebounds from a loss). We show that the unstable phase happens when there is a lack of confidence and seems to describe ``boom-bust'' periods in which changes in prices are exponential.