Take the 2-minute tour ×  Is it another way of saying the ground
state?  share|improve this question basically, although
sometimes people also intend for it to include the low-lying
collective excitations as well. –  wsc Jan 10 '12 at 15:56 @wsc
thanks, do you mean like spin waves? If the spin chain is in
equilibrium, if it is low energy, does it have to mean that it's
in its ground state? (Since spin waves are, according to
wikipedia, propagating disturbances in magnetic materials). – 
Space boy Jan 11 '12 at 14:55 Like spin waves, yes. For the
spin-1/2 Heisenberg chain there is no gap to make very long
wavelength excitations -- in fact, this means that for any
temperature $T>0$ the expected number of spin waves in
equilibrium diverges. This is (part of) the Mermin-Wagner
theorem. –  wsc Jan 11 '12 at 15:37 So for low dimensional
systems, ground states are of course interesting, but people
very much like to know about the low-lying excitations, and
whether they destroy the thermal stability of that ground st