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

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

2000-05-22

arxiv.org/abs/cond-mat/0005366v1

Phys. Rev. E 61, 2232-2240 (2000)

Physics

Condensed Matter

Statistical Mechanics

23pages, 7 ps figures

Scientific paper

10.1103/PhysRevE.61.2232

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 $0p_{0}^{*}$ the critical frontier is completely continuous; however, for $p_{0}=p_{0}^{*}$, 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 $p_{0}$.

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