Gibbsianness of fermion random point fields

Details Gibbsianness of fermion random point fields Gibbsianness of fermion random point fields

2005-03-19

arxiv.org/abs/math-ph/0503048v1

Physics

Mathematical Physics

24 pages

Scientific paper

We consider fermion (or determinantal) random point fields on Euclidean space $\mbR^d$. Given a bounded, translation invariant, and positive definite integral operator $J$ on $L^2(\mbR^d)$, we introduce a determinantal interaction for a system of particles moving on $\mbR^d$ as follows: the $n$ points located at $x_1,...,x_n\in \mbR^d$ have the potential energy given by $$ U^{(J)}(x_1,...,x_n):=-\log\det(j(x_i-x_j))_{1\le i,j\le n}, $$ where $j(x-y)$ is the integral kernel function of the operator $J$. We show that the Gibbsian specification for this interaction is well-defined. When $J$ is of finite range in addition, and for $d\ge 2$ if the intensity is small enough, we show that the fermion random point field corresponding to the operator $J(I+J)^{-1}$ is a Gibbs measure admitted to the specification.

Affiliated with

Also associated with

No associations

Rating

Gibbsianness of fermion random point fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gibbsianness of fermion random point fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gibbsianness of fermion random point fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-180257