A What Are Examples of Exotic Order-Disorder Phase Transitions?

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Exotic order-disorder phase transitions occur when a thermodynamic system transitions from a highly ordered state to a disordered state upon reaching a critical order parameter value. This transition is characterized by a gradual increase in the order parameter followed by a sharp decrease, contrasting with standard first-order transitions in Landau theory. The discussion highlights that certain materials, such as bismuth, antimony, ice, cast iron, and germanium, exhibit this behavior under increased pressure at a constant temperature, where the melting point decreases with pressure. The scenario described involves the potential minimum shifting right, as opposed to the left in typical first-order transitions. These insights suggest that highly ordered states may be thermodynamically unstable under specific conditions.
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I am looking for possible examples and a variant of Landau's theory of phase transitions for an exotic order-disorder phase transition, in which a thermodynamic system jumps into a disordered (or less orderly) state by reaching the maximum critical value of the order parameter. That is, in one phase, with a change in temperature or pressure, the order parameter first gradually increases and then sharply vanishes during the transition. I think that a highly ordered state, even in equilibrium systems, may turn out to be thermodynamically unstable.
 
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Could you say how your scenario is different from a standard first-order transition within Landau theory? I imagine the minimum of a potential (as a function or order parameter) moving the right or left while a local minimum centered at zero lowers in potential until it eventually becomes the global minimum.
 
the minimum of a potential moving the right, whereas in the standart first-order transition within Landau theory it moves left.
 
I think, I found this type of transitions. They are realized by increasing the pressure at a fixed temperature for substances with an anomalous dependence of the melting point on pressure (decreasing it with increasing pressure). Such substances include bismuth, antimony, ice, cast iron and germanium. In this case, the order parameter increases to the left of the transition, since the number of point defects of the Schottky and Frenkel type decreases with increasing pressure.
 
A relative asked me about the following article: Experimental observation of a time rondeau crystal https://www.nature.com/articles/s41567-025-03028-y I pointed my relative to following article: Scientists Discovered a Time Crystal That Reveals a New Way to Order Time https://www.yahoo.com/news/articles/scientists-discovered-time-crystal-reveals-180055389.html This area is outside of my regular experience. I'm interested in radiation effects in polycrystalline material, i.e., grain...

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