In a brief introduction to statistical mechanics, that is a part of a wider course on Solid State Physics I am taking, the teacher introduced the concept of microcanonical ensemble and the ergodic hypothesis, both in its general formulation as the equivalence between the average over time and the weighted average over the ensemble and in its application to the microcanonical ensemble as the fact that the distribution function is constant over all the accessible microstates corresponding to an equilibrium situation. In the lecture, he left somehow the idea that there is something not completely clear about this hypothesis, without pointing out what.
Studying Landau-Lifshitz "Course on Theoretical Physics, vol. 5", this hypothesis is somehow assumed to be wrong, even though it is used. Looking for a counter example to prove it wrong, on Wikipedia I found out that ferromagnetic materials in vacuum undergo a spontaneous symmetry breaking, exhibiting a magnetization and therefore a preferred set of microscopical configurations even though others, with the opposite direction of the magnetization vector, are possible, even in absence of any interaction.
Here comes my questions:
the symmetry breaking in ferromagnetic materials below the Curie temperature could take place due to some microscopic interactions with something that is neglected in our description? The first thing that came to my mind is the vacuum fluctuations of the electromagnetic field, that maybe could locally break the symmetry and induce a macroscopic symmetry break. Equivalently, this question could be rephrased as: do microcanonical systems actually exist?
the ergodic hypothesis does not say anything on how the system can pass from one microscopical configuration to another one. In my opinion, if between one configuration and the other there is an high enough barrier potential, the system will never change from one configuration to the other, while if we are neglecting (for non-microcanonical systems) interactions that can provide the energy needed for the system to cross this barrier, then the system could explore also this second configuration. Is it possible for the validity of the ergodic hypothesis to be related to the height of the energy barrier between allowed microscopic configurations? Again in the example of ferromagnetism, going from one direction of the magnetization to the other one will require an interaction between magnetic dipoles that is too high to be neglected, thus making the ergodic hypothesis not valid.
After a little further study, this problem seems to be related to what we have in the description of second order phase transitions given by Landau (and, in my case, applied to the example of magnetism considered and to superconductivity). Could a more complete description of phase transitions take into account the problem of spontaneous symmetry breaking? Is it something relevant to our limited knowledge of the system (if we knew every kind of interaction, we could predict it) or is it something much more deep and physically meaningful?