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This conference summary and outlook provides a personal overview of the topics and themes of the August 2009 Dresden meeting on quantum criticality and novel phases. The dichotomy between the local moment and the itinerant views of magnetism is revisited and refreshed in new materials, new probes, and new theoretical ideas. New universality and apparent zero temperature phases of matter move us beyond the old ideas of quantum criticality. This is accompanied by alternative pairing interactions and as yet unidentified phases developing in the vicinity of quantum critical points. In discussing novel order, the magnetic analogs of superconductivity are considered as candidate states for the hidden order that sometimes develops in the vicinity of quantum critical points in metallic systems. These analogs can be thought of as “pairing” in the particle–hole channel and are tabulated. This analogy is used to outline a framework to study the relation between ferromagnetic fluctuations and the propensity of a metal to nematic type phases – which at weak coupling correspond to Pomeranchuk instabilities. This question can be related to the fundamental relations of Fermi liquid theory.

Quantum criticality and novel phases: Summary and outlook