Analyticity and the phase diagram of QCD

Abstract

Some consequences of the analyticity of the free energy (pressure) of QCD at finite chemical potential are deduced. Lattice simulations at imaginary chemical potential are possible due to the positivity of the measure. We show that such a theory cannot be interpreted as a thermodynamic system with a phase diagram in the usual sense. However, simulations at imaginary chemical potential are useful because the free energy can be analytically continued and information on the thermodynamic system at real chemical potential can be extracted by two means—either by the usual method of Taylor expansions, or by using this data to extract Yang–Lee zeroes of the grand-canonical partition function. We also comment on the structure of zeroes expected for the usual picture of the phases of QCD, following a discussion of the physics of imaginary chemical potential.