Figure 1

(Color online) Illustration of the POM lattice. The blue (solid) bonds indicate $S^x{S}^x$ terms while the red (dashed) bonds stand for $S^z{S}^z$ links. The lattice is closely related to a checkerboard. The generalization to the 3D POM is straightforward with sublattices A and B being cubes rather than plaquettes.Reuse & Permissions

Figure 2

(Color online) Snapshots of the plaquette energy distribution on a $N=40\times 40$ lattice taken at $T=1.0$ and $T=0.02$, respectively. In the high-temperature regime (a) the system is disordered and a symmetry breaking has occurred in (b) for $T$ less than a critical temperature $T_{\text{c}}$. Darker regions (color) represent lower energy. Figures (c) and (d) are snapshots of configurations in spin space corresponding to the high- and low-temperature phases for $L=10$. No evident magnetic order is seen. The circles in (c) and (d) signify local energy density where darker means larger negative energy. Spins are color (gray) coded to make their direction more apparent.Reuse & Permissions

Figure 3

(Color online) Results from classical and quantum MC simulations for the 2D POM. (a) The order parameter $D$ for various lattice sizes $L=10$ to $L=96$ for the classical model employing periodic boundary conditions. The inset shows the plaquette structure factor $S_{\text{pl}}$ for $L=20$, $L=32$, and $L=42$. The order parameter indicates a clear crystallization effect for $T<0.086$. (b) The classical Binder parameter $B$ close to the transition temperature supporting a second-order phase transition. The inset shows the susceptibility $\chi$ on a logarithmic scale for $L\ge 16$. Generally, steeper curves in (a) and (b) correspond to larger lattice sizes. (c) The critical temperatures $T_{\text{c}}$ from FSS of the maxima locations of the susceptibility for both the classical and quantum cases and two different boundary conditions $\left(\text{open}=\text{obc},\text{periodic}=\text{pbc}\right)$.Reuse & Permissions

Figure 4

(Color online) FSS of the order parameter $D$ for a 2D system and for the slope $s_B$ of the Binder parameter for a 3D system. Both quantities are calculated at the critical temperatures and yield the expected Ising exponents.Reuse & Permissions

Figure 5

Plot of (a) the disorder-averaged (order) parameter ${\left[D\right]}_{\text{av}}$ and (b) the disorder-averaged Binder ratio ${\left[B\right]}_{\text{av}}$ versus temperature $T$ for $x=1\%$ site dilution in the classical case. The Binder parameter does not show any signature of a remaining phase transition for sizes up to $L=128$ and temperatures down to $T=0.03$. The critical temperature in the clean case is indicated by the arrow.Reuse & Permissions