Could someone recommend a book/resource where I can find a detailed way of sketching out a QCD temperature-chemical potential phase diagram using gap equations (eg. equations 35-37 or 39-40 as given here)?
P.S- Other similar questions on QCD phase diagrams focus more on their characteristics and not so much much on the basic method of obtaining them.
It is rather a complicated question and still an area of active research. The most reliable and direct way to plot the phase diagram with the axes $\mu, B, T$, where $\mu$ is baryon potential, $B$ is magnetic field is by means of Lattice QCD.
However, there is a important limitation - that the theory with baryon chemical potential suffers from notorious sign problem. This makes the direct simulation not feasible and results are obtained with imaginary chemical potential $i \mu$, and then analytically continued to the real axis. There also exist different approaches for handling the sign problem - reweighting, complex Langevin, but none of the gives fully satisfactory results.
As a not very recent but of a good quality review I recommend https://arxiv.org/abs/hep-lat/0701002v1.
