Simulating Complex Modulated Phases Through Spin Models

We extend the computational approach for studying striped phases on curved surfaces, presented in the previous talk, to two new problems involving complex modulated phases. First, we simulate a smectic liquid crystal on an arbitrary mesh by mapping the director field onto a vector spin and the density wave onto an Ising spin. We can thereby determine how the smectic phase responds to any geometrical constraints, including hybrid boundary conditions, patterned substrates, and disordered substrates. This method may provide a useful tool for designing ferroelectric liquid crystal cells. Second, we explore a model of vector spins on a flat two-dimensional (2D) lattice with long-range antiferromagnetic interactions. This model generates modulated phases with surprisingly complex structures, including 1D stripes and 2D periodic cells, which are independent of the underlying lattice. We speculate on the physical significance of these structures.