Hi Umesh,
At first, that seems to me like a very odd thing to do. What motivates
it in your case?
I say that because the cumulant expansion is a series expansion like,
for example, a Taylor expansion: each successive term is typically
supposed to be a smaller correction than the previous
Hi Scott,
Third cumulant in your example will not be zero because this arrangement is
symmetric only on the average. Locally, the interatomic pair potential (and the
cumulants are the measures of the effective pair potential) which is the sum of
the two potentials - between the interestitial
Hi Anatoly,
Your example is a slightly different model than the one I just
suggested. I'm taking the limit in which the lattice atoms are fixed
in place. In that case, symmetry demands the third cumulant to be
zero. In a case such as you describe, the lattice atoms themselves can
move
Thanks, Matt--you said that much more clearly than I did.
I'd add that, personally, I avoid using cumulants to account for
unresolved features when possible.
For example, suppose that a central metal atom is coordinated to six
oxygen atoms in an octahedral arrangement. But suppose also that
Matt, Scott:
There is a situation in one dimensional world, not so practically useful
though, where the third cumulant is zero. It describes the 1st nearest neighbor
interaction between a central atom (x) in the group of three atoms:
A-x-A. Indeed, here the third cumulant is zero, the
Anatoly,
You're right--3 dimensions ruins my symmetry argument. My mistake.
On the other hand, I still suspect that there exists a realistic case
where forcing the third cumulant to zero cause a much smaller increase
in chi-square than forcing the fourth cumulant to zero; e.g., a broad,
Hi Scott,
It could be an interesting direction, to use these type of lattice calculations
to predict, as you suggested, what type of structures (or host compounds, for
dopands), will, if not make it zero, which is probably impossible, but minimize
third cumulant. Thus, it may be a rational
