Landau Theory - Order parameter- Extensive or intensive?

[binbagsss]

Homework Statement

[/B]
1) Is the order paramter $\phi(x)$ intensive or extensive?
2) Is $M$ intensive or extensive?

With the following definitions :

Homework Equations

The Attempt at a Solution

1) Free energy is extensive, however I don' think I can use this to deduce whether $\phi(x)$ is intensive or extensive via (1) since it will depend on the exact form of $W(\phi)$

Some texts say it's intensive and others extensive.

For example :

2) I believe $H$ the external field is intensive; and so since $M$ is it's conjugate variable via $M=\frac{\partial A}{\partial H}$ , $M$ must be extensive?

Any help much appreciated.

 

[Fred Wright]

Say you have a block of material and you measure the magnetization to have a certain magnitude. Now you cut up the block into n equal pieces. Does the magnetization of each piece equal the magnetization of the whole block divided by n? If so it is extensive. Does the magnetization of each piece equal the magnetization of the whole block? If so it is intensive. Ask yourself the same questions by imagining that you could measure the order parameter.

 

[binbagsss]

Homework Statement

[/B]
1) Is the order paramter $\phi(x)$ intensive or extensive?
2) Is $M$ intensive or extensive?

With the following definitions :

View attachment 204112

Homework Equations

The Attempt at a Solution

1) Free energy is extensive, however I don' think I can use this to deduce whether $\phi(x)$ is intensive or extensive via (1) since it will depend on the exact form of $W(\phi)$

Some texts say it's intensive and others extensive.

For example :

View attachment 204111 View attachment 204110

2) I believe $H$ the external field is intensive; and so since $M$ is it's conjugate variable via $M=\frac{\partial A}{\partial H}$ , $M$ must be extensive?

Any help much appreciated.

Say you have a block of material and you measure the magnetization to have a certain magnitude. Now you cut up the block into n equal pieces. Does the magnetization of each piece equal the magnetization of the whole block divided by n? If so it is extensive. Does the magnetization of each piece equal the magnetization of the whole block? If so it is intensive. Ask yourself the same questions by imagining that you could measure the order parameter.

intensive.