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We present a treatment of the triangular lattice antiferromagnetic Ising model (TAFIM) based on a small number of elementary ideas common to statistical and solid-state physics. The TAFIM is represented as a reduced BCS model in one space, one (imaginary) time dimension. The representation is approximate for nonzero temperature, but allows quick derivation of asymptotically exact thermodynamic functions, and the divergence of the spin–spin correlation length. The fermionic representation is exact at zero temperature. We demonstrate the existence of a two-dimensional continuum of zero-temperature equilibrium macrostates characterized by satisfied bond fractions of the three different orientations, and calculate their entropy densities.

Recently discovered diamond nanothreads offer a stiff, sp 3 -hybridized backbone unachievable in conventional polymer synthesis that is formed through the solid-state pressure-induced polymerization of simple aromatics. This method enables monomeric A-B alternation to fully translate from co-crystal design to polymer backbone in a sequence-defined manner. Here, we report the compression of aryl:perfluoroaryl (Ar/ArF) co-crystals containing –OH and –CHO functional groups. We analyze the tolerance of these functional groups to polymerization, explore the possibility of keto–enol tautomerization, and compare the reaction outcomes of targeted solid-state Ar/ArF design on nanothread formation. Two new co-crystals comprising phenol:pentafluorobenzaldehyde (ArOH:ArFCHO) and benzaldehdye:pentafluorophenol (ArCHO:ArFOH) were synthesized through slow solvent evaporation. Analysis of the single-crystal structures revealed different hydrogen bonding patterns between the –OH and –CHO in each solid (tape and orthogonal dimers, respectively), in addition to markedly different π–π stacking distances within the Ar/ArF synthons. In situ Raman spectroscopy was used to monitor the compression of each co-crystal to 21 GPa and illustrated peak shifts for the –OH and –CHO stretching regions during compression. Photoluminescence corresponding to polymerization appeared at a lower pressure for the co-crystal with the smallest π–π stacking distance. Nevertheless, the recovered solid with the larger centroid : centroid and centroid : plane π–π stacking distancesmore »featured a diffraction ring consistent with the anticipated dimensions of a co-crystal-derived nanothread packing, indicating that both functional group interactions and parallel stacking affect the pressure-induced polymerization to form nanothreads. IR spectroscopy of the recovered samples revealed large shifts in the –OH & –CHO stretching regions, particularly noticable for ArCHO:ArFOH, which may reflect geometrical constraints associated with forming a rigid thread backbone under pressure. Simulation suggests that hydrogen bonding networks may affect the relative compressibility of the co-crystal along a thread-forming axis to modulate the propensity for nanothread formation.« less