# Sherrington-Kirkpatrick model with negative mean $J_0$

In the Sherrington-Kirkpatrick (SK) model, one considers an Ising Hamiltonian

$$H = -\sum_{i

where $$J_{ij}$$ are drawn independently from a Gaussian distribution with mean $$J_0$$ and standard deviation $$J$$.

In their original papers [1,2], SK obtain the phase diagram:

I followed all the steps of the derivation. However I don't understand how the phase diagram for negative $$J_0$$ is derived, because there is a change of variables involved where the square root of $$J_0$$ is taken which would give an imaginary result (see line before Eq.(9) in 1). I think some (perhaps trivial) modifications are needed to obtain the phase diagram for negative $$J_0$$.

So my question is: Assuming replica symmetry (as SK), how does one derive the phase diagram for $$J_0<0$$?

References