Random-field effects in spin models: Supersymmetry, criticality, and universality

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Statistical physics, one of the pillars of modern physics, describes how macroscopic experimental observations of a physical system (such as temperature and pressure) are related to microscopic variables, not seen with the naked eye. The beauty of the statistical physics approach lies in its ability to neatly describe phase transitions, such as ice melting, and other fundamental phenomena, including magnetism. However, the situation is more complicated: magnetic materials, which touch all technological aspects of our civilisation, contain impurities (disorder) that lead to unexplored properties and defy the standard framework. In fact, disorder is not only unavoidable in solid state materials and ubiquitous in realistic classical examples, but also quantum many-body systems. Disorder is responsible for a variety of interesting novel phenomena that do not have clean counterparts, such as the Anderson localisation, exotic quantum critical points, and glassy phases of matter, that appear solid on a short time scale, but continuously relax towards the liquid state. These phenomena are present in a wide range of condensed matter systems including polymers, metallic alloys, magnetic spin glasses, and many soft materials such as colloids, foams, emulsions or other complex fluids.Understanding the effects of frustration and quenched disorder in condensed matter physics has immense technological consequences that reach up to the design and construction of quantum annealing devices used for future technologies of quantum computers. A vast amount of research has failed to reveal the physical mechanisms at play due to the rough energy landscape of these systems that disarms analytical and numerical approaches. Fortunately, years of consistent effort have enabled us to develop exceptionally versatile tools, including some extremely powerful numerical and theoretical approaches, that have unblocked the path towards a direct attack on the problem. Using this new toolbox of methods, the proposed project aims at clarifying the effects of random fields, one of the most common yet less understood types of disorder with many experimental analogues in physics, on a variety of spin models and unveiling their critical behaviour and universality principles. In addition, we also intend to clarify other ambiguous theoretical conjectures, like supersymmetry and dimensional reduction. We expect our results to pave the way for novel experiments and technological breakthroughs made possible by the development of an unambiguous interpretation of the underlying phenomena. As the concepts used for deciphering complexity in disordered systems apply to other fields involving emerging collective behaviour (e.g., financial markets, social networks), the progress achieved will underpin advancements in other scientific areas as well.