A frustrated system is one where the interactions compete with each other and cannot be simultaneously satisfied. Such situations can occur in magnets, where the elementary constituents are spins (magnetic moments) and their interactions take the form of exchange or dipolar couplings. With antiferromagnetic interactions, favoring antialignment of nearby spins, and certain spatial arrangements (particularly those involving triangles, such as the pentagram shown on the right), it is impossible to minimize the interaction energy on every link at the same time. This situation can lead to two possible outcomes.

The first is that the spins nonetheless find some compromise configuration that minimizes the thermodynamic free energy globally. Because there may be numerous ways of resolving the incompatible interactions, this can lead to a diversity of different ordered configurations and a rich phase structure. In addition, weaker effects such as lattice distortions or quantum fluctuations can have significant effects when the a priori dominant interactions are deadlocked.

The second possibility is that the system remains disordered even at low temperatures. The resulting state, with persistent large fluctuations despite strong correlations between the degrees of freedom, is referred to as a spin liquid. In the case of a quantum spin liquid, this behavior persists to zero temperature, sustained by quantum fluctuations. Experimental examples of spin liquids are known in the classical spin ice materials, such as holmium titanate, and there is strong evidence for a quantum spin liquid in the mineral herbertsmithite. Among the exotic features of such spin liquids are fractionalized excitations, taking the form of magnetic monopoles in the specific case of spin ice, and topological order.

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Ising spins on the Nordita logo