Punctures and p-spin curves from matrix models III. Dl type and logarithmic potential

The intersection numbers for p spin curves of the moduli space M(g,n) are considered for D type by a matrix model. The asymptotic behavior of the large genus g limit and large p limit are derived. The remarkable features of the cases of p= 1/2, - 1/2, -2, -3 are examined in the Laurent expansion for multiple correlation functions. The strong coupling expansions for the negative p cases are considered.