Studies of low temperature magnetism on "Toblerone" lattices

材料的物理性质一般取决于它们各自的成分。然而，现代物理学已经表明，由许多物体组成的系统，尽管它们的原子组成成分不同，但它们可以表现出类似的宏观现象，而且统计力学已被证明在揭示造成这种现象的微观机制方面非常机智。磁学是统计力学成功的一个显著例子；物理学家可以利用统计力学的方法来研究磁体最有趣的性质。在这里，我们提出了一种由正多边形堆叠组成的磁晶格的理论研究，我们的目标是描述它们的低温行为，目的是提供有助于理解复杂材料的简单模型。根据我在肯特大学的硕士项目的研究结果，我们首先关注材料的物理性质通常取决于它们的单个成分。然而，现代物理学已经表明，由许多物体组成的系统，尽管它们的原子组成成分不同，但它们可以表现出类似的宏观现象，而且统计力学已被证明在揭示造成这种现象的微观机制方面非常机智。磁学是统计力学成功的一个显著例子；物理学家可以利用统计力学的方法来研究磁体最有趣的性质。在这里，我们提出了一种由正多边形堆叠组成的磁晶格的理论研究，我们的目标是描述它们的低温行为，目的是提供有助于理解复杂材料的简单模型。根据我在肯特大学（University of Kent）硕士项目的发现，我们首先关注ising模型。具体来说，我们的目标是具有单轴各向异性的自旋的相图，这些自旋排列在等边三角形的顶点上，一个平行于另一个堆叠，它们之间的距离恒定。研究在这个模型中发现的一些热力学量的不寻常行为——例如比热——是否可能是非常规相变的表现，确实是至关重要的。由于最近对类似模型[2]的关注，我们的目标是开发更丰富的替代方案来描述这些晶格的复杂变化的低温行为，这在文献中尚未研究过。模型。具体来说，我们的目标是具有单轴各向异性的自旋的相图，这些自旋排列在等边三角形的顶点上，一个平行于另一个堆叠，它们之间的距离恒定。研究在这个模型中发现的一些热力学量的不寻常行为——例如比热——是否可能是非常规相变的表现，确实是至关重要的。由于最近对类似模型[2]的关注，我们的目标是开发更丰富的替代方案来描述这些晶格的复杂变化的低温行为，这在文献中尚未研究过。

The physical properties of materials depend in general on their individual constituents. Modern physics,however, has shown that systems of many bodies can feature analogous macroscopic phenomena despitetheir different atomistic constituents, and statistical mechanics has proved to be very resourceful for shedding light on which microscopic mechanisms are responsible for such phenomena. Magnetism is a strikingexample of the success of statistical mechanics; physicists may study the most intriguing properties of magnets by use of methods from statistical mechanics. Here we propose a theoretical study of magnetic latticeswhich consist of stacking of regular polygons, and we target the characterisation of their low-temperaturebehaviour with the aim to provide simple models that could help the understanding of complex materials.Developing on the findings from my masters project at the University of Kent, we begin by focusing on theThe physical properties of materials depend in general on their individual constituents. Modern physics,however, has shown that systems of many bodies can feature analogous macroscopic phenomena despitetheir different atomistic constituents, and statistical mechanics has proved to be very resourceful for shedding light on which microscopic mechanisms are responsible for such phenomena. Magnetism is a strikingexample of the success of statistical mechanics; physicists may study the most intriguing properties of magnets by use of methods from statistical mechanics. Here we propose a theoretical study of magnetic latticeswhich consist of stacking of regular polygons, and we target the characterisation of their low-temperaturebehaviour with the aim to provide simple models that could help the understanding of complex materials.Developing on the findings from my masters project at the University of Kent, we begin by focusing on theIsing model. Specifically, we target the phase diagram of spins with uniaxial anisotropies which are arrangedat the vertices of equal equilateral triangles stacked one parallel to the other with a constant distance between them. It is indeed crucial to investigate whether the unusual behaviour of some of thermodynamicallyquantities found for this model - for example the specific heat - could be a manifestation of unconventionalphase transitions [1]. Further motivated by recent attention given to similar models [2], we aim to developricher alternatives to describe the low temperature behaviour of complex variations of such lattices, as yetunstudied in the literature. model. Specifically, we target the phase diagram of spins with uniaxial anisotropies which are arrangedat the vertices of equal equilateral triangles stacked one parallel to the other with a constant distance between them. It is indeed crucial to investigate whether the unusual behaviour of some of thermodynamicallyquantities found for this model - for example the specific heat - could be a manifestation of unconventionalphase transitions [1]. Further motivated by recent attention given to similar models [2], we aim to developricher alternatives to describe the low temperature behaviour of complex variations of such lattices, as yetunstudied in the literature.