Ising spin glass in a random network with a Gaussian random field

We investigate thermodynamic phase transitions of the joint presence spin glass (SG) and random field (RF) using a graph model that allows us to deal with quenched disorder. Therefore, connectivity becomes controllable parameter in our theory, allowing answer what differences are between this description mean-field theory i.e., fully connected theory. have considered network Ising where exchange interaction as well RF variables following Gaussian distribution. The results were found within replica symmetric (RS) approximation, whose stability is obtained two-replica method. This also puts work context broader discussion, which RS function connectivity. In particular, show for small there region at zero temperature solution remains stable above given value magnetic no matter strength RF. Consequently, important crossover SG regimes predicted by