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  1. Is order parameter for a phase transition is unique?
  2. Is it always true that in one phase order parameter have zero value and in another phase it has non zero value?
  3. Is there any standard rules for chosing order parameters?
  4. Can a system undergoing phase transition can have more than one order parameter?
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Order parameter is defined as a quantity that is zero in one phase and not zero in the other - this answers the second question, but also the first one, since any quantity satisfying this condition can be an order parameter. In particular, if $M$ is an order parameter, then any function of $M$ that leaves it zero in one phase and non-zero in the other is also an order parameter.

To my knowledge there are no standard rules, since the order parameter is often a physical property, specific to the system considered (e.g., magnetization for ferromagnet, density for liquid-gas transition, etc.)

As systems may have very complex phase diagrams, there may be multiple order parameters, controlling where on the phase diagram the system finds itself. See an example in the figure below (taken from here) enter image description here

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  • $\begingroup$ In principle, valid order parameters can accidentally be zero even within the ordered phase - these are fine-tuned points, though. $\endgroup$ Oct 25, 2022 at 11:56
  • $\begingroup$ Thank you for the response. $\endgroup$ Jan 4, 2023 at 15:06
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    $\begingroup$ @SitaChettri if this response is satisfactory, please consider accepting it! $\endgroup$ Dec 14, 2023 at 14:46

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