The competition between spin glass, ferromagnetism and Kondo effect is analysed here in a Kondo lattice model with an inter-site random coupling Jij between the localized magnetic moments given by a generalization of the Mattis model [15] which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with Grassmann fields have been used to obtain the partition function. The static approximation and the replica symmetric ansatz have also been used. The solution of the problem is presented as a phase diagram giving T /J versus JK /J where T is the temperature, JK and J are the strengths of the intrasite Kondo and the intersite random couplings, respectively. If JK /J is small, when temperature is decreased, there is a second order transition from a paramagnetic to a spin glass phase. For lower T /J, a first order transition appears between the spin glass phase and a region where there are Mattis states which are thermodynamically equivalent to the ferromagnetism. For very low T /J, the Mattis states become stable. On the other hand, it is found as solution a Kondo state for large JK /J values. These results can improve the theoretical description of the well known experimental phase diagram of CeN i1−xCux [8,9,10,11].
A symmetrically dilute Hopfield model with a Hebbian learning rule is used to study the effects of gradual dilution and of synaptic noise on the categorization ability of an attractor neural network with hierarchically correlated patterns in a two-level structure of ancestors and descendants. Categorization consists in recognizing the ancestors when the network has been trained exclusively with the descendants. We consider a macroscopic number of ancestors, each with a finite number of descendants, and take into account the stochastic noise produced by the former in an equilibrium study of the network, by means of replica-symmetric mean-field theory. Phase diagrams are obtained that exhibit a categorization, a spin-glass, and a paramagnetic phase, as well as the dependence of the order parameters on the relevant quantities. The de Almeida-Thouless lines that limit the validity of the replica-symmetric results are also obtained. It is shown that gradual dilution increases considerably the region where a stable categorization phase may be found.
The competition among spin glass (SG), ferromagnetism and Kondo effect has been analysed in a Kondo lattice model where the inter-site coupling Jij between the localized magnetic moments is given by a generalized Mattis model [5] which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with of Grassmann fields has been used to obtain the partition function. The static approximation and the replica symmetric ansatz has also been used. The solution of the problem is presented as a phase diagram temperature T versus JK (the strength of the intra-site interaction). If JK is small, for decreasing temperature there is a second order transition from a paramagnetic to a spin glass phase For lower temperatures, a first order transition appears where solutions for the spin glass order parameter and the local magnetizations are simultaneously non zero. For very low temperatures, the local magnetizations becomes thermodinamically stables. For high JK , the Kondo state is dominating. These results could be helpful to clarify the experimental situation of CeN i1−xCux [1,2].
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