Laminated and desiccated siliceous dolostones, dolomitic mudstones and dolomitic sandstones in the Cambrian Parakeelya Alkali Member of the Observatory Hill Formation accumulated in an alkaline playa. Four facies are recognized (from lake centre to lake edge): lake, saline mudflat, dry mudflat and sandflat facies. The facies occur in cycles. Cycles of tens of metres thickness record the gradual expansion and contraction of the playa. Superimposed smaller cycles of tens of centimetres thickness record minor oscillations in the position of the strandline in a shallow lake. The dominance of saline mudflat, dry mudflat and sandflat facies indicates that the lake was rimmed by broad flat areas with negligible relief. The high δ18O values of primary and penecontemporaneous diagenetic carbonates of +24 to +28‰ (SMOW) indicate strong evaporation of ground and surface waters within the lake system. Calcite pseudomorphs of the sodium carbonate minerals trona and shortite have δ18O values between + 19 and + 22.5‰, and contain fluid inclusions with variable salinites and homogenization temperatures up to around 110°C. This suggests that the euhedral alkaline evaporites were dissolved by heated waters; calcite pseudomorphs then precipitated from a mixed solution formed by the interaction of these incoming fluids with the relatively saline interstitial brines. The sodium bicarbonate solutions formed by dissolution of the evaporites would have been dispersed by the basinal brines so that despite the closed drainage, further groundwater concentration did not take place.

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Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a simple generalisation of this idea to Z N -symmetric models. In 1989 Baxter discovered a non-Hermitian but PT -symmetric model directly generalising the Ising chain which was much later recognised by Fendley to be a free parafermion spectrum. By extending the model's magnetic field parameter to the complex plane, we show that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general PT -symmetric at these exceptional points, their proximity can have a profound impact on the model on the PT -symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field). Contents 5 Other Degeneracies of H 11 6 Exceptional Points and Positive Real λ 11 7 Conclusion 12

Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a generalisation of this idea to \mathbb{Z}_NℤN-symmetric clock models. In 1989 Baxter discovered a non-Hermitian but \mathcal{PT}𝒫𝒯-symmetric model directly generalising the Ising chain, which was later described by Fendley as a free parafermion spectrum. By extending the model’s magnetic field parameter to the complex plane, it is shown that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general \mathcal{PT}𝒫𝒯-symmetric at these exceptional points, their proximity can have a profound impact on the model on the \mathcal{PT}𝒫𝒯-symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field).

No abstract