Qualitative theory for first- and second-order lattice phase transitions in quasi-one-dimensional systems

The occurrence of first-order dimer phase transitions (PT) in quasi-one-dimensional lattice coupled anisotropic spin systems and one- and two-band Hubbard systems is studied. It is shown that a certain degree of exchange anisotropy of the $s=\frac{1}{2}$ Heisenberg chains is needed to obtain first-order PT. The first-order spin-dimer PT of the zig-zag chains in V${\mathrm{O}}_2$ is explained as a consequence of geometric constraints. The first-order metal-insulator PT observed in V${\mathrm{O}}_2$ is explained by means of the two-band Hubbard model. For the charge-transfer salts it is argued that a polarization instability is associated with the first-order spin-dimer PT which requires the isotropic Heisenberg model to be modified. The so far unexplained magnetic-excitation gap observed in uniformly stacked tetramethyl-$p$-phenylenediamine-tetracyanoquinodimethane (TMPD-TCNQ) crystals is attributed to a spin-polarization instability.