# System-size dependent phase transitions

I noticed that some physical phenomena require a system of size above some critical value to be observed. Two examples I know are:

Do you know more examples?

• Theoretically, as the system size $N \to \infty$, some zeros of partition function $Z$ approaches to real axis, and hence phase transition is possible. So I guess the threshold or critical value depends on how fast those zeros approaches to real axis. – K_inverse Sep 6 '18 at 9:06
• I am not sure the question is really answerable: for small systems, it becomes very delicate to provide clear-cut definitions of phases and, a fortiori, of phase transitions... – Yvan Velenik Sep 6 '18 at 14:24
• @YvanVelenik thank you for your comment. Please note that I'm not asking for general statements/theorems... I asked for examples similar to the one I propose, if possible. – m137 Sep 6 '18 at 17:33