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

自旋模型中的随机场效应：超对称性、临界性和普遍性

• 批准号: EP/X026116/1
• 负责人: Nikolaos Fytas
• 金额: $ 39.02万
• 依托单位: University of Essex
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX026116%2F1
• 关键词: Random; field; effects; spin; models

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.

统计物理学是现代物理学的支柱之一，它描述了物理系统（例如温度和压力）的宏观实验观察如何与肉眼看不到的微观变量相关。统计物理方法的优点在于它能够巧妙地描述相变，例如冰融化和其他基本现象，包括磁性。然而，情况更为复杂：磁性材料涉及我们文明的所有技术方面，其中含有杂质（无序），这些杂质会导致未开发的特性并违反标准框架。事实上，无序不仅在固态材料中不可避免、在现实经典例子中普遍存在，而且在量子多体系统中也是如此。无序导致了各种有趣的新奇现象，这些现象没有干净的对应物，例如安德森局域化、奇异的量子临界点和物质的玻璃相，它们在短时间内呈现固态，但不断松弛到液态。这些现象存在于各种凝聚态物质系统中，包括聚合物、金属合金、磁性自旋玻璃和许多软材料，如胶体、泡沫、乳液或其他复杂流体。了解凝聚态物理中挫败和淬灭无序的影响具有巨大的技术影响，影响到用于未来量子计算机技术的量子退火设备的设计和构造。由于这些系统的粗糙能量景观削弱了分析和数值方法的武装，大量研究未能揭示起作用的物理机制。幸运的是，经过多年的不懈努力，我们能够开发出异常通用的工具，包括一些极其强大的数值和理论方法，为直接解决问题开辟了道路。使用这个新的方法工具箱，拟议的项目旨在阐明随机场（最常见但鲜为人知的无序类型之一，在物理学中具有许多实验类似物）对各种自旋模型的影响，并揭示其关键行为和普遍性原则。此外，我们还打算澄清其他模糊的理论猜想，例如超对称性和降维。我们期望我们的结果能够为新颖的实验和技术突破铺平道路，通过对潜在现象的明确解释而使这些实验和技术突破成为可能。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），因此所取得的进展也将支撑其他科学领域的进步。