Emilio, plz halp

When one reads a popular science book how much of the stuff actually gets stored in brain. Any or none? Do I have to read several times? Does anybody do that?

@JohnRennie !

I guess it’s just for fun! Nothing fruit ful can be achieved by it!

I was reading about force fields of michio kaku.

@DanielSank the exponent is a sum of quadratic terms so it's a quadratic form in $\mathbf{x}$. It must be positive definite and the prefactor must be right because it's a probability distribution

if you want to check it explicitly you don't actually have to sum that many terms, just extract the non-zero matrix elements. If I have time later I'l write an answer

On the other hand correlation functions (es spin-spin) are the moments (or cumulants) of the generating function. To get the power law behaviour I must find that these correlation functions are the Fourier transform of a non analytic function (othervise the space x correlation function would decrease exponentially, as it does far from the critical point)

The bridge between the two statements I guess is that the derivatives of the termodinamic potentials are the cumulants of the generating function. But these cumulants to me give the space x correlation function and not it's fourier transform in k-space which has the non analyticities. Am I saying some non sense? is there something I can look up for some formal argument about this question?

@fqq "Just extract the non-zero matrix elements". Right but now?

In quantum ensembles, is one of the constraints conservation of energy?

As in $E$ is a constant

or do we say $\langle E \rangle$ is a constant?