  This paper is the second in a pair treating a new lattice model for nematic
media. In addition to the familiar isotropic (I) and nematically ordered (N)
phases, the phase diagram established in the previous paper (Paper I) contains
a new, topologically ordered phase (T) occuring at large suppression of
topological defects and weak nematic interactions. This paper (Paper II) is
concerned with the experimental signatures of the proposed phase diagram.
Specific heat, light scattering and magnetic susceptibility near both the N/T
and I/T transitions are studied, and critical behavior determined. The singular
dependences of the Frank constants ($K_1$, $K_2$, $K_3$) and the dielectric
tensor anisotropy ($\Delta \epsilon$) on temperature upon approaching the N/T
transition are also found.
