Abstract
We give an elementary and pedagogical review of the phase diagrams which are possible in quantum chromodynamics (QCD). Herein, emphasis is upon the appearance of a critical endpoint, where disordered and ordered phases meet. In many models, though, a Lifshitz point also arises. At a Lifshitz point, three phases meet: disordered, ordered, and one in which spatially inhomogeneous phases arise. At the level of mean field theory, the appearance of a Lifshitz point does not dramatically affect the phase diagram. We argue, however, that fluctuations about the Lifshitz point are very strong in the infrared and significantly alter the phase diagram. We discuss at length the analogy to inhomogeneous polymers, where the Lifshitz regime produces a bicontinuous microemulsion. We briefly mention the possible relevance to the phase diagram of QCD.
Highlights
Experiments at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC)have demonstrated conclusively that a new state of matter is produced in the collisions of heavy ions at high energy
The system behaves like a quark–gluon plasma (QGP) at high temperature and very small baryon chemical potential
We discuss what appears to be a minor feature in the phase diagram: the appearance of spatially inhomogeneous phases
Summary
Experiments at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). We discuss what appears to be a minor feature in the phase diagram: the appearance of spatially inhomogeneous phases In nuclear matter, these are the familiar pion and kaon condensates. The appearance of such phases is difficult to derive, even in mean field theory These phases are certainly important, naively, one would not expect such condensates to dramatically affect the phase diagram. It is possible that the critical endpoint is completely wiped out, leaving only a line of first-order transitions In this case, while infrared fluctuations can be strong in the infrared, they remain finite at all points in the phase diagram. We discuss the close analogies between the phase diagram of quantum chromodynamics (QCD) and that of inhomogeneous polymers [6,7] In this regard, what we call the Lifshitz regime is known as bicontinuous microemulsions and is of practical importance
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