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   Hang, Nguyen T.; Mordukhovich, Boris S.; Sarabi, M. Ebrahim (March 2020, Mathematical Programming)
3. Second order Zeeman interaction and ferroquadrupolar order in TmVO4

   https://doi.org/10.1038/s41535-022-00475-1  

   Vinograd, I.; Shirer, K. R.; Massat, P.; Wang, Z.; Kissikov, T.; Garcia, D.; Bachmann, M. D.; Horvatić, M.; Fisher, I. R.; Curro, N. J. (June 2022, npj Quantum Materials)

   Abstract TmVO₄exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity. A magnetic field oriented along thec-axis constitutes a transverse effective field for the quadrupolar order parameter, continuously tuning the system to a quantum phase transition as the field is increased from zero. In contrast, in-plane magnetic fields couple to the order parameter only at second order, such that orienting along the primary axes of the quadrupole order results in an effective longitudinal field, whereas orienting at 45 degrees results in a second effective transverse field. Not only do in-plane fields engender a marked in-plane anisotropy of the critical magnetic and quadrupole fluctuations above the ferroquadrupolar ordering temperature, but in-plane transverse fields initially enhance the ferroquadrupolar order, before eventually suppressing it, an effect that we attribute to admixing of the higher crystalline electric field levels. 

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5. Connecting Higher-Order Separation Logic to a First-Order Outside World

   https://doi.org/10.1007/978-3-030-44914-8_16  

   William Mansky, Wolf Honoré (April 2020, Programming Languages and Systems. ESOP 2020)

   Separation logic is a useful tool for proving the correctness of programs that manipulate memory, especially when the model of memory includes higher-order state: Step-indexing, predicates in the heap, and higher-order ghost state have been used to reason about function pointers, data structure invariants, and complex concurrency patterns. On the other hand, the behavior of system features (e.g., operating systems) and the external world (e.g., communication between components) is usually specified using first-order formalisms. In principle, the soundness theorem of a separation logic is its interface with first-order theorems, but the soundness theorem may implicitly make assumptions about how other components are specified, limiting its use. In this paper, we show how to extend the higher-order separation logic of the Verified Software Toolchain to interface with a first-order verified operating system, in this case CertiKOS, that mediates its interaction with the outside world. The resulting system allows us to prove the correctness of C programs in separation logic based on the semantics of system calls implemented in CertiKOS. It also demonstrates that the combination of interaction trees + CompCert memories serves well as a lingua franca to interface and compose two quite different styles of program verification. 

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