Absence of Replica Symmetry Breaking in the Random Field Mixed-Spin Ginzburg-Landau Model

Abstract: In this paper, an extension of the random field Ginzburg-Landau model on the hypercubic lattice is considered by adding $p$-spin ($p\geqslant 2$) interactions coupled to general disorders. This new model is called the random field mixed-spin Ginzburg-Landau model. We proved that, in the infinite volume limit of this model, the variance of spin overlap vanishes.