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I have come across the concept of phase transitions in various contexts. From simple phase transition between different states of matter like water to ice and so on, to phase transition in magnetic materials from the Ising model and metal-insulator transition like the one proposed Sir Nevill Mott.

What is the generalized abstract definition of a phase transition?

Can anyone explain, what exactly are phase transitions in these specific cases given above and more?

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    $\begingroup$ I think you should consult a book on thermodynamics or statistical thermal physics or both. Basic idea is that at a phase transition there is a re-ordering of the structure, leading to a discontinuity in the equilibrium entropy or one of its derivatives, as a function of some other macroscopic variable such as temperature or applied field. $\endgroup$ – Andrew Steane Feb 28 at 16:17
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    $\begingroup$ to enlarge slightly upon @AndrewSteane's comment, there's a lot of cool physics involved in phase transitions generally, and the study of phase transitions has yielded mathematical models of them which among other things furnish schemes for placing them in different classes and so forth. $\endgroup$ – niels nielsen Feb 28 at 21:37
  • $\begingroup$ @nielsnielsen Could you tell me more about them? Are you referring to the Ising model and Lars Onsager's exact solution to the problem? $\endgroup$ – EverydayFoolish Mar 1 at 3:06
  • $\begingroup$ @AndrewSteane How do you differentiate between these Phase transitions? $\endgroup$ – EverydayFoolish Mar 1 at 3:07
  • $\begingroup$ @EverydayFoolish, I last studied them 45 years ago, so I am not the guy you should talk to- but there's lots written about them that's available out there. $\endgroup$ – niels nielsen Mar 1 at 5:33

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