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The effects of random magnetic fields are considered in an Ising spin-glassmodel defined in the limit of infinite-range interactions. The probabilitydistribution for the random magnetic fields is a double Gaussian, whichconsists of two Gaussian distributions centered respectively, at $+H_{0}$ and$-H_{0}$, presenting the same width $\sigma$. It is argued that such adistribution is more appropriate for a theoretical description of real systemsthan its simpler particular two well-known limits, namely the single Gaussiandistribution ($\sigma \gg H_{0}$), and the bimodal one ($\sigma = 0$). Themodel is investigated by means of the replica method, and phase diagrams areobtained within the replica-symmetric solution. Critical frontiers exhibitingtricritical points occur for different values of $\sigma$, with the possibilityof two tricritical points along the same critical frontier. To our knowledge,it is the first time that such a behavior is verified for a spin-glass model inthe presence of a continuous-distribution random field, which represents atypical situation of a real system. The stability of the replica-symmetricsolution is analyzed, and the usual Almeida-Thouless instability is verifiedfor low temperatures. It is verified that, the higher-temperature tricriticalpoint always appears in the region of stability of the replica-symmetricsolution; a condition involving the parameters $H_{0}$ and $\sigma$, for theoccurrence of this tricritical point only, is obtained analytically. Some ofour results are discussed in view of experimental measurements available in theliterature.

Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines