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accurately describes fluctuations about the isotropic phase. We then consider expansions about the ordered state, comparing static correlations obtained analytically within the Frank approximation with our numerical re- sults. 

We use a finite-difference discretisation with nearest- neighbour stencils for gradients and the Laplacian. We implement periodic boundary conditions. Specifically, in three dimensions, we consider a box of dimension L$_{x}$, L$_{y}$ and L$_{z}$ along the Cartesian directions, and grid these lengths with equal grid spacing Δ x = Δ y = Δ z = 1. The latter defines lattice units for the spatial coordi- nate. We define corresponding discrete time units for the temporal variables by choosing Δ t = 1. Fourier modes are labelled by the wave-vector q = ( q$_{x}$, q$_{y}$, q$_{z}$ ), where each component is of the form q$_{α}$ = 2 πn$_{α}$/L$_{α}$ , with n$_{α}$ = 0 , 1 , 2 , . . . , ( L$_{α}$ − 1). With this discretisation, the Laplacian in Fourier space 

is given by 

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The nearest-neighbour finite difference stencil suffers from lack of isotropy at high wavenumbers. This can be improved through the use of higher-point stencils [17–19]. 

Applying the method of lines discretisation to Eq. (3) reduces it to a system of stochastic ordinary differential equations, whose Fourier representation in the harmonic approximation of Eq. (11) is 

The Fourier representation of the drift-diffusion dynam- ics is encoded in the linear operator D , 

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Fourier representations of the one and two-dimensional method of lines discretisations are obtained by setting the corresponding wavenumbers to zero. The static and dynamic autocorrelations in Fourier space follow in a straightforward manner though the replacement of q 2 by its discrete Laplacian representation. The results are 

It is also useful to define an angle-averaged structure fac- 

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