Universality of Replica-Symmetry Breaking in the Transverse Field Sherrington–Kirkpatrick Model

The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to with a general random exchange interactions. relation between expectation value of interaction energy and Duhamel correlation function spin operators can be obtained by an approximate integration parts In addition Falk-Bruch inequality, these explicit evaluations enable us prove that variance overlap two replica does not vanish under sufficiently weak low temperature. absence ferromagnetic long range order also shown distinguish RSB from $\mathbb Z_2$-symmetry breaking.