Indeed, the Libertarians do CLAIM to be the party that best expresses
his philosophy, and maybe they are the one that "best" does that -- but
much of libertarian theory is pretty far from TJ, IMO.  TJ was stronger on
popular sovereignty -- government formed and influenced by "the will of
the people" -- than the Libertarians are.  TJ emphasized national self-
government (by the people en masse), whereas the Libertarians
emphasize individual rights in opposition to any kind of national
government.  TJ was never so "individualistic," although he, of course,
believed that the rights of every individual member were the foundation
of a free society ("ALL men are created equal").  It's a subtle difference,
and it is interesting to try to capture and define it, hence my going on at
length once you get me started. ;-)

The Libertarians are too "doctrinaire" for my taste.  They adhere to a
political "doctrine" rather than a political "system" -- another subtle
difference between the L's and TJ.  TJ believed in self-government by
the people, and his philosophical principles were aimed basically at
implementing that -- at having a society directed by a free people; the
L's believe in government that is limited by certain dogmatic ideas, and
those philosophical principles ARE their basic aim.  One empowers a
living organism (people) politically; the other directs a political
organization (government) by certain political ideas.