The difference between order parameter and state parameter?

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SUMMARY

The discussion centers on the distinction between order parameters and state parameters within the context of Landau theory. State parameters, such as pressure (P), temperature (T), and volume (V), are essential for describing a thermodynamic system. In contrast, the order parameter is treated as an external parameter rather than an independent variable, despite its role in expanding free energy into a power series. The conversation highlights that while the order parameter can be influenced by other thermodynamic variables, it is often analyzed alongside temperature in phase transition scenarios.

PREREQUISITES
  • Understanding of Landau theory of phase transitions
  • Familiarity with thermodynamic variables (P, T, V)
  • Knowledge of free energy concepts in thermodynamics
  • Basic grasp of order parameters in statistical mechanics
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  • Explore the role of order parameters in various phase transitions
  • Study the relationship between thermodynamic variables and order parameters
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Physicists, particularly those specializing in statistical mechanics and thermodynamics, as well as students studying phase transitions and their implications in various physical systems.

Diracmai
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At first, we need some state parameters(like P/T/V) to fully describe a system. And the order parameter is also a parameter which could describe the property of the system.
However, in the Laudau theory, why it said that order parameter is an external parameter(not a independent variable)? Is there any different between order parameter and state parameters(like P/T/V etc.)?
 
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I would say no, as in Landau theory we expand the free energy into a power series in the order parameter. Hence it must be a thermodynamic variable.
 
DrDu said:
I would say no, as in Landau theory we expand the free energy into a power series in the order parameter. Hence it must be a thermodynamic variable.
Ok! Actually, I also take the some viewpoint as you. In addition, I have another question.Generally, when we use Laudau phase transition theory, we always choose T and order parameter as free energy's variables. In this condition, it that means we hold other thermodynamic variable as constant and only discuss the relation between order parameter and temperature. In fact, the order parameter can also be the function of other thermodynamic variables.
 
Diracmai said:
In fact, the order parameter can also be the function of other thermodynamic variables.
Isn't this trivial? E.g. you can describe a gas in terms of V and T or in terms of p and T, the transformation being P(T,V). So you can always introduce the order parameter as an independent thermodynamic variable.
 

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