Studies of low temperature magnetism on "Toblerone" lattices

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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.