Errata for "Replica calculations for the SK model"

This post lists errata for the note Replica calculations for the SK model of Haozhe Shan.

1. Eq. (13) in page 2:
   The first item on the exponential should be .

2. The line below Eq. (25) in page 4:
   It might be Now as

3. Eq. (37) in page 5:
   The factor is missing in the right-hand side of the equal sign.

4. Eq. (47) in page 6:
   The sign of integration in the third term is missing.

   Besides, in Eq. (47), it seems that the equivalence relation

   is used to obtain the third term from the second term. However, I don’t know if this limit is correct, or if it’s done in some other way.

5. Eq. (51) in page 6:
   I believe that the result of the last integral should not use the approximately equal sign, omitting the coefficient , since it is important for the value of the ground state entropy (although this does not change the sign).

6. The equation at the bottom of page 10:
   The second term on the exponential in the second line and the first term in the third line should be instead of .

7. Eq. (74) (86) in page 11:
   The item on the exponential of all these equations should be corrected to without an additional .

8. Eq. (75) in page 11:
   The variable is missing on the exponential.

9. Eq. (96) in page 12:
   The sign before the last term should be rather than .

10. The equation at the bottom of page 12:
    The third and fifth lines are repeated with the second and fourth lines respectively.
    I guess you want to express

    on the third line.

11. Eq. (102) and (103) in page 13:
    A square bracket should be placed after the second summation sign to indicate the summation of all subsequent terms, to avoid misunderstandings.