%0 Thesis %A O'Hare, Anthony %D 2018 %T The formation of low-temperature superstructures in the two-dimensional Ising model with next-nearest neighbour interactions %U https://repository.lboro.ac.uk/articles/thesis/The_formation_of_low-temperature_superstructures_in_the_two-dimensional_Ising_model_with_next-nearest_neighbour_interactions/9410495 %2 https://repository.lboro.ac.uk/ndownloader/files/17028107 %K untagged %K Physical Sciences not elsewhere classified %X For several decades the formation of different kinds of superstructures in solids has been a topical issue in condensed matter physics. The superstructures (or spatially modulated structures) may be of a different nature: magnetic patterns like spin-density waves, inhomogeneous charge distributions in charge-ordered compounds, dipolar and quadrupolar ordering in ferroelectrics or ferroelastics, regular lattice distortions and related orbital structures, stripe-like arrangements of dopants in alloys, etc. The phase diagrams of such compounds can be rather complicated involving a large number of phases with non-trivial types of ordering. Fortunately, all this wealth of seemingly unrelated phenomena can be often described by rather simple models with a due account taken of a competitive character of the most important interactions. In this thesis I will investigate the Ising model in 2-D with nearest and next-nearest neighbour interactions using several methods including exact diagonalisation of small clusters, transfer matrix technique and Monte Carlo simulation of large lattices. [Continues.] %I Loughborough University