Systems with a $mathbb{Z}_2$ spontaneous symmetry breaking transition?

Question

I am studying spontaneous $mathbb{Z}_2$ symmetry breaking transition for some time now in quantum (transverse-field) and classical Ising systems. I would like to look beyond my little box in terms of realisations of this Ising universality in other physical systems.
Therefore I would like to start a discussion/collection on this platform of all kinds of physical systems displaying spontaneous $mathbb{Z}_2$ symmetry breaking transition.
My explicit question is:
Which systems have a $mathbb{Z}_2$ spontaneous symmetry breaking transition?
I would be very happy for examples from all across the spectrum of realisations with references to look them up in detail.
Thank you all in advance for your suggestions.

*I am not sure if this question is appropriate for StackExchange as I have seen similar questions been taken down quite fast. If the community does not like open questions of this type just let me know it.

Senya Shlosman · Answer

Let me point to one example of $Bbb Z_2$ symmetry breaking. It is contained in my paper
S. Shlosman: Phase transitions for two-dimensional models with isotropic short-range interactions and continuous symmetry, Comm. Math. Phys. 71(1980), 207-212.
There I consider a 2D system with $O(2)$ symmetry group (which is disconnected). In agreement with the Mermin-Wagner theorem, the $SO(2)$ part of the symmetry is not broken, while the remaining $Bbb Z_2$ symmetry is broken, at low temperatures.

Systems with a $mathbb{Z}_2$ spontaneous symmetry breaking transition?

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