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I've just started studying phase transitions and symmetry breaking for my PhD and I've met something I'd like to understand better. When we study the local potential vs. the order parameter in a structural phase transition I see there are two limiting cases, the one in which the potential barrier is much greater than thermal fluctuations and the one in which it's much smaller, the first one leading to order-disorder transitions and a dynamical structure factor with 'relaxation' shape, the second one leading to displacive phase transitions and a 'phonon' dynamical structure factor. I can see why this happens (in second case system can oscillate between the two minima thanks to thermal fluctuations, in first case it can't), but how is it derived formally? I want to know because I'd like to make calculations about what happens if, instead, potential energy barrier and thermal fluctuations are of the same order. Thanks for your help!

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# Phase transitions: from the potential to the dynamical structure factor ?

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