Reciprocal-space correlation functions of nearest-neighbour spin ice

Reciprocal-space correlation functions \(\langle \sigma_\mu(k)\sigma_\nu(-k)\rangle\) of the nearest-neighbour spin ice Hamiltonian \(H = J \sum_{\langle ij\rangle} \sigma_i\sigma_j\) on the pyrochlore lattice, from Monte Carlo simulations on 128×128×128 cubic unit cells.

File formats

The file name indicates the temperature (in units of J) where the measurement was taken.

Files with extension .dat contain the correlation functions as double-precision complex floats.
Files with extension .err contain the standard errors as single-precision real floats.

Both file types contain an array of shape (4, 4, 128, 256, 256). The meaning of the indices (from major to minor):

sublattice index μ

sublattice index ν

wave vector components in units of \(2\pi/(128a_0)\)

The sublattice indices correspond to the site offsets \(r_0 = [111]/8, r_1=[1\bar1\bar1]/8, r_2=[\bar11\bar1]/8,r_3=[\bar1\bar1 1]/8\) from the nearest FCC lattice point. For the Fourier transforms, all sublattices are shifted to these lattice points, so the correlators stored in the files are periodic with respect to the FCC reciprocal lattice.

The wave vector range covered is \(0\le k_x< 2\pi/a_0, 0\le k_y,k_z< 4\pi/a_0\), an (unconventional) reciprocal-space unit cell of the FCC pyrochlore lattice.

The utility loader.py loads the files, shapes them in the correct array format, and extracts single k-points.

Details of data generation

We performed Monte Carlo simulations of nearest-neighbour spin ice using the efficient loop-string algorithm introduced in Phys. Rev. B 90, 220406(R). For nonzero temperatures, correlations between different strings were excluded, which effectively averages all spin configurations compatible with a given loop graph. We ran 32 independent Markov chains at each temperature point and obtained 4096 Monte Carlo samples in each. The reported standard errors are the error on the mean of the 32 Markov chains.