Ising spin glass under continuous-distribution random magnetic fields:   Tricritical points and instability lines
  The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered respectively, at $+H_{0}$ and $-H_{0}$, presenting the same width $\sigma$. It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely the single Gaussian distribution ($\sigma \gg H_{0}$), and the bimodal one ($\sigma = 0$). The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of $\sigma$, with the possibility of 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 in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that, the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters $H_{0}$ and $\sigma$, for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature. 
N. Crokidakis, F. D. Nobre