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A novel model, devised to describe spontaneous chirality synchronization in complex liquids and liquid crystals, is proposed and studied. Segments of ribbon-like molecular columns with left- or right-handed 180degree twist lie on the bonds of a honeycomb lattice so that three ribbons meet in a vertex of the hexagonal honeycomb. The energy of each vertex is a minimum if the three ribbons have the same chirality, -E, and is +E otherwise, and the ground state is homochiral, i.e. all ribbons have the same hand. The energy levels for two vertices linked by a single ribbon are either -2E, 0 and +2 E in this vertex model. Monte Carlo simulations demonstrate that this model is identical to an Ising spin model on a Kagome lattice, for which the site energy structure is quite different. The equivalence of the ordering of the vertex and Ising spin models is also shown analytically. The energy difference between the disordered and ground states, 4J in the spin model, is related to the transition temperature for the Kagome lattice using the exact result, Tc=2.14J. The ordering energy difference for a single site is 50% higher for the vertex model. The thermodynamic energy for the vertex model is corrected by a factor of 1/3 due to double counting and this makes the specific heat of the vertex model also equal to that of the spin model as expected. Other similar models where there is an unusual relation between the site and thermodynamic energies are discussed briefly., Comment: 17 pages, 9 figures

Antiferromagnetically coupled Ising s =3 spins on a triangular lattice are very close to ordering at zero temperature. The low temperature behaviour of a triangular lattice with Ising spins s =3 has been simulated by using both Glauber and Kawasaki dynamics. The formation of misfit clusters, which are essential for destabilizing the ordered state, are inhibited by the use of Kawasaki dynamics. The sublattice susceptibilities and the sublattice order parameter are found to depend qualitatively on the dynamics used so that robust ordering occurs when Kawasaki dynamics are employed. The thermal behaviour that is found for the spin model with Kawasaki dynamics gives insight into the observed ordering of side chains seen in a tetraphilic liquid crystal., Comment: 10 pages 3 figures

We have performed Monte Carlo simulations to investigate the temperature dependence of the ordering of the side chains of the X-shape liquid crystal molecules which are arranged in a hexagonal array. Each hexagon contains six side chains, one from each side of the hexagon. Each liquid crystal molecule has two, dissimilar, side chains, one that contains silicon and one containing fluorine. Like chains attract each other more strongly than unlike chains and this drives an order-disorder transition. The system is frustrated because it is not possible to find a configuration in which all the hexagons are occupied by either all silicon or all fluorine chains. There are two phase transitions. If only pairwise interactions are included it is found that there is a novel fluctuating phase between the disordered phase and the fully ordered ground state. This did not agree with the experiments where an intermediate phase was seen that had long range order on one of the three sublattices. Agreement was found when the calculations were modified to include attractive three body interactions between the silicon chains., Comment: Accepted in Physical Review E 26 pages including 7 figures

This paper has a pedagogical introduction. We describe the correct method for performing Monte Carlo simulations of Ising model systems with spin greater than one half. Correct and incorrect procedures are clearly outlined and the consequences of using the incorrect procedure are shown. The difference between Kawasaki and Glauber dynamics is then outlined and both methods are applied to the antiferromagnetic square and triangular lattices for S =1., Comment: 12 pages, 4 figures

Landau theory is used to investigate the behaviour of a metallic magnet driven towards a quantum critical point by the application of pressure. The observed dependence of the transition temperature with pressure is used to show that the coupling of the magnetic order to the lattice diverges as the quantum critical point is approached. This means that a first order transition will occur in magnets (both ferromagnets and antiferromagnets) because of the coupling to the lattice. The Landau equations are solved numerically without further approximations. There are other mechanisms that can cause a first order transition so the significance of this work is that it will enable us to determine the extent to which any particular first order transition is driven by coupling to the lattice or if other causes are responsible., Comment: 12 pages including 5 figures, to be presented at MMM-Intermag conference and accepted for publication in Journal of Applied Physics

A dynamic model of the asymmetric Ising glass is presented: an Ising model with antiferromagnet bonds with probabilities q arranged at random in a ferromagnetic matrix. The dynamics is introduced by changing the arrangement of the antiferromagnetic bonds after n Monte Carlo steps but keeping the same value of q and spin configuration. In the region where there is a second order transition between the ferromagnetic and paramagnetic states the dynamic behaviour follows that expected for motional narrowing and reverts to the static behaviour only for large n. There is a different dynamic behaviour where there is a first order transition between the ferromagnetic and spin glass states where it shows no effects of motional narrowing. The implications of this are discussed. This model is devised to explain the properties of doped ZnO where the magnetisation is reduced when the exchange interactions change with time., Comment: Paper was presented at MMM 2008 and is accepted for publication in J.A.P