Effect of geometrical frustration on inverse freezing

The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor $\left(J_1\right)$ and second-neighbor $\left(J_2\right)$ intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings $\left(J\right)$ among clusters. We obtain phase diagrams of temperature versus $J_1/J$ in two cases: the absence of $J_2$ interaction and the isotropic limit $J_2=J_1$, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of $J_1/J$ in both cases. The $J_1$ interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF.

Figure 1

Results for clusters without GF $\left(r=0\right)$. (a) Phase diagrams of $T/J$ vs $J_1/J$ for several cluster sizes, where the solid and dashed lines indicate second- and first-order transitions, respectively. Cluster shapes are also presented. (b) Entropy per spin as a function of temperature for $n_s=16$. The inset exhibits the entropy as a function of $J_1/J$.

Figure 2

Intracluster first-neighbor correlation as a function of $J_1/J$ for several cluster sizes without GF. The cluster shapes are the same as in Fig. 1.

Figure 3

Results for clusters with GF $\left(r=1\right)$. (a) Phase diagrams of $T/J$ vs $J_1/J$, where solid and dashed lines represent first- and second-order transitions, respectively. (b) Entropy per spin as a function of $J_1/J$ for $T/J=0.07$. Insets show the entropy as a function of $r$ at $T/J=0.07$ for the SG and PM phases when $n_s=12$ and 20. The cluster shapes are the same as Fig. 1.