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The magnetic systems with disorder form an important class of systems, whichare under intensive studies, since they reflect real systems. Such a class ofsystems is the spin glass one, which combines randomness and frustration. TheSherrington-Kirkpatrick Ising spin glass with random couplings in the presenceof a random magnetic field is investigated in detail within the framework ofthe replica method. The two random variables (exchange integral interaction andrandom magnetic field) are drawn from a joint Gaussian probability densityfunction characterized by a correlation coefficient $\rho$. The thermodynamicproperties and phase diagrams are studied with respect to the naturalparameters of both random components of the system contained in the probabilitydensity. The de Almeida-Thouless line is explored as a function of temperature,$\rho$ and other system parameters. The entropy for zero temperature as well asfor non zero temperatures is partly negative or positive, acquiring positivebranches as $h_{0}$ increases.

physica a statistical mechanics and its applications

The Sherrington-Kirkpatrick spin glass model in the presence of a random  field with a joint Gaussian probability density function for the exchange  interactions and random fields