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How does both hold:

Coleman-Mermin-Wanger theorem continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions $d\le2$

There are observable systems with an effective 1D reaction coordinate that go under phase transitions, like proteins or Spin-Glass.

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?

Here are more examples of 1D systems which have phase transitions: Kittel’s Model and 1D Ising Model.