Fig. 6: Map of regimes with different spatial magnetic correlations.
From: Machine-learning-assisted insight into spin ice Dy2Ti2O7
The map is generated by varying J3 and \(J_{3^\prime}\), with the remaining Hamiltonian parameters J1, J2, and D being fixed to their optimal values. The colors in a indicate different groups of S(Q), which correspond to regimes with different patterns of magnetic correlations. b–i Simulated S(Q) data sliced in the high symmetry plane at specific points indexed on panel (a). The large dark-blue regime (1) corresponds to long-range ferromagnetic order, as indicated by the Bragg peaks in panel (b). c–i Correspond to different patterns of short-range correlations arising from subsets of states that still obey ice rules. The pattern (g) falls within the same orange regime as Hopt, and qualitatively captures the Coulombic correlations expected for spin ice [cf. experimental scattering data in Fig. 3a].
