Inverse freezing in the Ghatak-Sherrington model with a random field

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from the GS model without a RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field $D$, is gradually suppressed when the RF is increased.

Figure 1

Order parameters as a function of temperature for $D/J=0$ (upper panel), $D/J=0.5$ (lower panel), and several values of $\Delta$.

Figure 2

Phase diagrams of temperature versus $\Delta /J$ for $D/J=0.0$ (full line) and $D/J=0.5$ (dashed line).

Figure 3

Phase diagrams of temperature versus $D/J$ for several values of $\Delta$. Panels (b), (c), and (d) show details of the first order transitions. The dashed-dotted lines at low $T$ are extrapolations to the $T=0$.

Figure 4

Entropy as a function of temperature (region where the re-entrance occurs) for three values of $\Delta$ and $D$. The first order temperature is equal to $T_{1f}=0.1J$ for all curves.

Figure 5

Panel (a) shows the average number of sites with nonmagnetic states $n_0$ versus $D/J$ for $T/J=0.1$ and several values of $\Delta /J$. Panel (b) shows $n_0$ versus $T/J$ for three values of $D/J$ and $\Delta /J$. The values of $D/J$ in panel (b) are chosen in order to present the first order temperature equal to $T_{1f}=0.1J$. $T_f$ represents the freezing temperature.