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，描述了物理系统（例如温度和压力）的宏观实验观察与微观变量有关，而肉眼未见。统计物理学方法的美丽在于它能够整洁地描述冰融化和其他基本现象（包括磁性）等相变的能力。但是，情况更加复杂：触摸我们文明的所有技术方面的磁性材料都包含杂质（混乱），这些杂质（无序）导致未开发的特性并违背了标准框架。实际上，在固态材料中不可避免地是不可避免的，在现实的古典示例中无处不在，而且是量子多体系统。疾病负责各种有趣的新型现象，这些现象没有干净的对应物，例如安德森定位，奇异的量子临界点和物质的玻璃阶段，它们在短时间内表现出固体，但持续朝向液态。这些现象存在于广泛的冷凝物系统中，包括聚合物，金属合金，磁性旋转玻璃以及许多软材料，例如胶体，泡沫，乳液或其他复杂的流体。理解挫败感和冷凝物物理学中淬火障碍的影响具有巨大的量子和构造技术的巨大技术后果。由于这些系统的粗糙能量格局，大量的研究未能揭示出发挥作用的物理机制。幸运的是，多年的一致努力使我们能够开发出极具通用的工具，包括一些非常有力的数值和理论方法，这些工具却没有阻止直接攻击该问题的道路。拟议的项目使用了这种新的方法箱，旨在阐明随机领域的影响，这是最常见但知识较低的疾病类型之一，具有物理学的许多实验类似物，在各种旋转模型上，并揭示其关键行为和普遍性原理。此外，我们还打算阐明其他模棱两可的理论猜想，例如超对称性和尺寸还原。我们希望我们的结果为新的实验和技术突破铺平了道路，从而发展了对基本现象的明确解释。由于无序系统中用于破译复杂性的概念适用于涉及新兴集体行为（例如金融市场，社交网络）的其他领域，因此所取得的进步也将支持其他科学领域的进步。