Competing interactions are a prerequisite for geometrical frustration. One well-known example of frustration are Ising spins on triangular corner-sharing plaquettes as for example on the Kagome lattice in 2 dimensions, leading to an extensive ground state degeneracy.  But what happens when different disordered phases co-exist and compete between each other?  By using the same triangular building blocks as for Kagome, we consider the so-called Shuriken lattice (also known as Square-Kagome lattice), which shows, contrary to Kagome, inequivalent sites belonging to loops of different sizes, namely 4 and 8. The presence of these two types of loops together with a large unit-cell offers a natural setting to tune the anisotropy in order to explore a variety of phases.
In order to shed light on this question,we investigated thermodynamic properties of the Ising model of the anisotropic Shuriken lattice using classical Monte Carlo simulations, analytical Husimi tree calculations and exact decoration-iteration transformation. By tuning the anisotropy of the lattice, it was possible to observe a reentrant behavior between disordered regimes from a high-temperature paramagnet to a classical spin liquid into a low-temperature binary paramagnet (BPM in the Fig.). The term ”binary paramagnet” illustrates the fact that the corresponding highly-degenerate ground state is made of two different types of uncorrelated (super-) spins. We round off our studies with an analytical method mapping the Shuriken lattice onto a checkerboard lattice with temperature dependent coupling parameters, giving insights into dominant competing interactions within the ordered and disordered regimes.

This work was published as “Reentrance of disorder in the anisotropic shuriken Ising model”, Rico Pohle, Owen Benton, and L.D.C. Jaubert, Phys. Rev. B 94, 0144290 (2016)