Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state

To referees: I thank you for your feedback, constructive comments, and careful reading of my manuscript. Your insights were extremely helpful, and I have applied the feedback where appropriate in the manuscript. I believe I addressed all the issues raised by all three reviewers, with just two exceptions.

Referee 1 wrote ``at the beginning of section 6.2, "of the baryon chemical potential" → "of the baryon number density"``. In this sentence I indeed meant baryon chemical potential.
Referee 3 suggested adding the $\gamma$ critical exponent to Table 1. I considered this but decided against it for consistency, as I would also need to include $R_\chi$. Adding two additional rows might distract the reader, given that these quantities are not the main focus of this lecture note. Instead, I have included references to the papers from which the data for $R_\chi$ and $\gamma$ were taken.

Figures:
Fig 9 and Fig 14 was modified as suggested be Referee 1: the extra "i" was removed from the y axes.

Equations:
1) To make equations a bit simple and more transparent, I rewrote Eq. (39) for Ising universality class only (that is substituted $N=1$).
2) I corrected Eq. (5), as the first referee suggested.

Here are some minor text changes (this list does not include trivial typos):
Page 4: In the beginning of the page "positive integer" -> "positive odd integer, as suggested by Referee 1.
Page 7: Reference [7] was added in a paragraph before Eq. (15), as suggested by Referee 2.
Page 8: A paragraph (at the very top of the page) on the universality of the magnetic equation of state and the location of the YLE singularity was added, as requested by Referee 2.
Page 9: In the middle of the page, Reference [12] was added to the sentence "For this reason, M. Fisher dubbed Yang-Lee edge singularities protocritical points [12]", as was requested by Referee 2.
Page 10: Before equation 25. Reference [10] was added, as was requested yb Referee 2.
Page 14: At the end of the first paragraph the sentence " The state of the art, six loop calculations of the critical exponents in ϵ-expansion can be found in Ref. [18]." was added as requested by the Referee 2 .
Page 14: A discussion on the calculation of the edge exponent in epsilon expansion was added one paragraph below Eq.(39) as requested by the Referee 2:
"Note, however, that in contrast to the YLE location, the edge exponent can be and was computed within ϵ expansion near 6 dimension (the upper critical dimension of φ^3 theory). For the state of the art, five-loop calculation, see Ref. [21]."
Page 14: As was requested by Referees 2 and 3, footnote 14 was added to address why epsilon expansion fails for the location of the YLE. Reference [19] was added as well.
Page 18: The following text was added to the table caption: Rχ and γ are taken from Refs. [31, 54] and Refs. [48, 55].
Page 20: Extra factors of "i" were removed when referring to "Im" parts of various quantities, as Referee 1 suggested.
Page 24: Footnote 19 was added to clarify that $N_\tau=8$ data was computed using single point Pade, as Referee 3 suggested.
Page 27: $\omega$ was switched to $w$ everywhere where appropriate, as Referee 1 suggested.