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    Tricritical Points in the Sherrington-Kirkpatrick Model in the Presence of Discrete Random Fields

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    The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. The model is studied through the replica method and phase diagrams are obtained within the replica-symmetry approximation. It is shown that the border of the ferromagnetic phase may present first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising ferromagnet under a trimodal random field, it is verified that the first-order phase transitions are directly related to the dilution in the fields (represented by p0p_{0}). The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for 0<p0<p0∗≈0.308560<p_{0}<p_{0}^{*} \approx 0.30856, a single tricritical point occurs, whereas if p0>p0∗p_{0}>p_{0}^{*} the critical frontier is completely continuous; however, for p0=p0∗p_{0}=p_{0}^{*}, a fourth-order critical point appears. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified; in particular, the Almeida-Thouless line in the plane field versus temperature is shown to depend on the weight p0p_{0}.Comment: 23pages, 7 ps figure
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