Title: Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model,
Abstract: It is proved that replica symmetry is not broken in the transverse and
longitudinal random field Ising model. In this model, the variance of spin
overlap of any component vanishes in any dimension almost everywhere in the
coupling constant space in the infinite volume limit. The weak
Fortuin-Kasteleyn-Ginibre property in this model and the Ghirlanda-Guerra
identities in artificial models in a path integral representation based on the
Lie-Trotter-Suzuki formula enable us to extend Chatterjee's proof for the
random field Ising model to the quantum model.