This is general question for physics understanding:
Following figure is the magnetization curves of a one-dimensional spin 1/2 trimerized J_1-J_1-J_2 Heisenberg quantum spin model in magnetic field in z direction, at different temperatures for lattice size N= 12 spins.
Black Curve corresponds to zero temperature T=0, in which Magnetization increases in steps. Reasons for step like magnetization is attributed to to finite number of spins, which is explanatory to me. Steps like feature completely disappears in the limit of large N
Red and Blue Curve are the magnetization at finite temperature. As you can see from the figure that in contrast to zero magnetization curve (black curve), steps starts disappearing in magnetization as Temperature T is increased from zero.
Could anyone here please explain me the "disappearance of step like feature in magnetization curve as Temperature T is increased from zero.
Generally steps (plateaus) in magnetization curves are due to the presence of gaps in the many body energy spectrum. Sometimes these gaps can survive to the thermodynamic (N\rightarrow \infty) limit but as you correctly point out, other gaps can be due to finite-size effects (small N limit).
These finite-size gaps are very small generally, and go to zero exponentially quickly with increasing N.
At the same time, the effect of increasing temperature is to average over more states, so it tends to “wash out” effects due to energy gaps once the temperature is around the size of a certain gap.
So when the gaps in question are small, then even for a small finite temperature any effects due to these gaps will be averaged over. That’s my explanation for why the steps (which are gap-driven effects) are removed once your temperature is increased even a small amount.
Note that even very robust steps or plateaus, which are stable to large N, will also eventually become smoothed out for high enough temperature too. It’s just that it would take a larger temperature for those usually.
