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

Physics Asked on August 7, 2021

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.

One 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.

Answered by Senya Shlosman on August 7, 2021

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