How does both hold:
continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions $d\le2$
For example below there is a 1D system with 2 phases state:
Here we have the energy landscape of protein folding which can be study by 1 reaction coordinate and has a few different phases:
How comes there are systems with $d \le 2$ that have phase transitions and why doesn't it contradict the Mermin-Wagner theorem? How is it related to Noeather's theorem?