Following is the m-h curve at various temperatures for a spin chain model. It can be seen that m=1/3 magnetization plateau disappears at T=0.3 J_1. From this data I wanted to draw T-h phase diagram showing the disappearance of plateau in that, Now the difficulty is how to choose the beginning h_{c_1} and end points (h_{c_2}) of plateau as it gets more and more curved with increasing temperature. how can I do that ? One possibly could be to count the beginning/end point at some \delta value down to m=1/3 line, or may be derivative could be helpful.
or is there any other way to draw the said diagram from other than this T dependent m-h curves.
Maybe this answer is too late to be helpful, but I would have the following thoughts about how you might be able to define the extent of your plateaus.
Of course in a strict sense the plateau sizes here are not well-defined, so any definition will be somewhat arbitrary. The most important thing is explaining in a paper what definition you chose and why.
One approach could be to take the regions where the magnetization is changing rapidly (like the steps) and fit them to a straight line. Then put another straight line at the plateau value. Where these two lines intersect could be the edge of the plateau.
Another approach could be to look at the second derivative and see where it changes sign.
