  We propose a simpler approach to identifying the limit of free energy in a
vector spin glass model by adding a self-overlap correction to the Hamiltonian.
This avoids constraining the self-overlap and allows us to identify the limit
with the classical Parisi formula, similar to the proof for scalar models with
Ising spins. For the upper bound, the correction cancels self-overlap terms in
Guerra's interpolation. For the lower bound, we add an extra perturbation term
to make the self-overlap concentrate, a technique already used in [Probab.
Math. Phys., 2(2):281-339, Ann. Inst. Henri Poincar\'e Probab. Stat.,
59(3):1143-1182] to ensure the Ghirlanda-Guerra identities. We then remove the
correction using a Hamilton-Jacobi equation technique, which yields a formula
similar to that in [Ann. Probab., 46(2):865-896]. Additionally, we sketch a
direct proof of the main result in [Electron. J. Probab. 25(23):1-17].
