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The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realise a fully-packed two-colour loop model in three dimensions. We present a detailed analysis of the statistics of these loops, which avoid themselves and other loops of the same colour, and contrast their behaviour to an analogous two-dimensional model. The properties of another extended degree of freedom are also addressed, flux lines of the emergent gauge field of the Coulomb phase, which appear as Dirac strings in spin ice. We mention implications of these results for related models, and experiments.
Motivated by a recent adsorption experiment [M.O. Blunt et al., Science 322, 1077 (2008)], we study tilings of the plane with three different types of rhombi. An interaction disfavors pairs of adjacent rhombi of the same type. This is shown to be a s
We study the interplay between magnetic frustration and itinerant electrons. For example, how does the coupling to mobile charges modify the properties of a spin liquid, and does the underlying frustration favor insulating or conducting states? Suppo
We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz-Thouless (KT) transitions for both the half-vortices and ordinary
A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped
Phase transitions, compensation phenomenon and magnetization of a ferro-ferrimagnetic ternary alloy AB$_{rho}$C$_{1-rho}$ composed of three different kinds of magnetic ions A, B and C with the spin magnitude 1/2, 1 and 3/2 are examined within the fra