This question is more about the maths than the physics.(adsbygoogle = window.adsbygoogle || []).push({});

So I am reading the textbook by Bergersen and Plischke, and they get the following:

$$m= \tanh [ \beta (qJm+h)]$$

where ##m## is the magnetization, ##q## is the number of nearest neighbours of site ##0##, ##J## and ##h##are the coefficients in the Hamiltonian: ##H = -J\sum_{<ij>} \sigma_i \sigma_j -h \sum_i \sigma_i##;

For the question, they write that ##m(h,T) ## satisfies: ##m(h,T) = -m(-h,T)##;

but I tried to showed this and I didn't succeed.

Here's my attempt:

$$-m(-h,T) = -\tanh [ \beta(-qJm(-h,T)-h) ] = m(-h,T)$$

I used the fact that ##\tanh(-x) = -\tanh(x)##.

Am I wrong?

Did they mean something else here?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Weiss molecular field theory

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**