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

Abstract

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 $p_0$). The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for $0<p_0<p_0^{\ast }\approx 0.30856$, a single tricritical point occurs, whereas if $p_0>p_0^{\ast }$ the critical frontier is completely continuous; however, for $p_0=p_0^{\ast }$, 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 $p_0$.

23pages, 7 ps figures

References in corpus (1)

• Evidence for the droplet/scaling picture of spin glasses

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