  In the frameworks of a nesting model for Q1D organic conductor at the
antiferromagnetic (SDW) quantum critical point the first-order transition
separates metallic state from the soliton phase having the periodic domain
structure. The low temperature phase diagram also displays the 2nd-order
transition line between the soliton and the uniformly gapped SDW phases. The
results agree with the phase diagram of (TMTSF)$_2$PF$_6$ near critical
pressure [T. Vuletic et al., Eur. Phys. J. B 25, 319 (2002)]. Detection of the
2nd-order transition line is discussed. We comment on superconductivity at
lowest temperature.
