Magnetic materials and models of magnetic systems have long provided physicists with an exquisite platform to investigate the general, at times even universal, principles that govern collective phenomena at phase transitions in systems of interacting degrees of freedom. Frustration is a generic term that encapsulates numerous phenomena where two or more types of microscopic interactions compete in driving the development of correlations in a system. An example is where strong short-range attraction competes with weak long-range repulsion. This is thought to arise, for example, in the core of neutron stars. There, the short range attractive strong force tend to condense neutrons and protons together. Ultimately, however, the agglomeration of positively charged protons is forestalled by the long-range electrostatic Coulomb repulsion, giving rise to complex density-modulated nuclear matter - a so-called "nuclear pasta". Frustration arises in strongly correlated electron systems, type-II superconductors in an applied magnetic field, liquid crystalline materials, molecular solids, etc. Yet, perhaps the simplest manifestation of frustration arises in magnetism. For example, magnetic moments (spins) that reside on the sites of a regular triangular lattice and interact with an antiferromagnetic coupling are unable to find a minimum energy state in which any given spin has all its nearest neighbours pointing in the opposite direction. Indeed, as Wannier showed in Phys. Rev. 79 (2): 357-364 (1950), a system of antiferromagnetically coupled Ising spins (that can only point in two opposite directions) on a triangular lattice shows no transition to long range order down to absolute zero temperature, unlike the ferromagnetic counterpart, and exhibits an extensive zero-temperature entropy. From our past experience with conventional magnetic systems, one expects that the study of frustrated magnetism can teach us, physicists, about the fundamental, new and broad principles at work among frustrated condensed matter systems.
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