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

统计物理学是现代物理学的支柱之一，它描述了一个物理系统(如温度和压力)的宏观实验观测与肉眼看不到的微观变量之间的关系。统计物理方法的美妙之处在于，它能够巧妙地描述相变，如冰川融化，以及其他基本现象，包括磁性。然而，情况更为复杂：磁性材料触及我们文明的所有技术方面，含有杂质(无序)，导致未开发的属性，并无视标准框架。事实上，无序不仅在固态材料中是不可避免的，在现实的经典例子中也是无处不在的，量子多体系统也是如此。无序是各种有趣的新奇现象的罪魁祸首，这些现象没有干净的对应物，例如安德森定域化、奇异的量子临界点和物质的玻璃相，这些现象在短时间尺度上看起来是固态的，但不断地向液态松弛。这些现象存在于广泛的凝聚态系统中，包括聚合物、金属合金、磁性自旋玻璃，以及许多软材料，如胶体、泡沫、乳液或其他复杂流体。了解凝聚态物理中的受挫和猝灭无序的影响具有巨大的技术后果，可延伸到用于未来量子计算机技术的量子退火器的设计和建造。由于这些系统粗糙的能量格局，解除了分析和数值方法的武装，大量的研究未能揭示起作用的物理机制。幸运的是，多年来的始终如一的努力使我们能够开发出特别多才多艺的工具，包括一些极其强大的数字和理论方法，为直接解决这一问题开辟了道路。利用这一新的方法工具箱，拟议的项目旨在澄清随机场对各种自旋模型的影响，并揭示它们的临界行为和普适性原理。随机场是最常见但鲜为人知的无序类型之一，在物理学中有许多实验类似物。此外，我们还打算澄清其他模棱两可的理论猜想，如超对称性和降维。我们希望我们的结果为新的实验和技术突破铺平道路，这些实验和技术突破是通过对潜在现象进行明确解释而实现的。由于用于破译无序系统复杂性的概念适用于涉及新兴集体行为的其他领域(例如金融市场、社交网络)，所取得的进展也将支持其他科学领域的进步。

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.