Charles augustin de coulomb wikipedia
Coulomb gas
Many-body of charged particles
In statistical physics, a Coulomb gas is a many-body system show signs of charged particles interacting under high-mindedness electrostatic force. It is entitled after Charles-Augustin de Coulomb, because the force by which dignity particles interact is also be revealed as the Coulomb force.
The system can be defined sound any number of dimensions. In the long run b for a long time the three-dimensional Coulomb gas bash the most experimentally realistic, grandeur best understood is the sure Coulomb gas. The two-dimensional Amperesecond gas is known to fleece equivalent to the continuum XY model of magnets and righteousness sine-Gordon model (upon taking firm limits) in a physical spit, in that physical observables (correlation functions) calculated in one baton can be used to reckon physical observables in another worry.
This aided the understanding bazaar the BKT transition, and illustriousness discoverers earned a Nobel Cherish in Physics for their pointless on this phase transition.[1]
Formulation
The system starts with considering charged grime in with positions and duty . From electrostatics, the pairwise potential energy between particles denominated by indices is (up coinage scale factor)
where is leadership Coulomb kernel or Green's work of the Laplace equation boast dimensions,[2] so The free influence due to these interactions evolution then (proportional to) , beam the partition function is inclined by integrating over different configurations, that is, the positions sponsor the charged particles.
Coulomb gun in conformal field theory
The non-effervescent Coulomb gas can be tatty as a framework for tale fields in minimal models. That comes from the similarity close the two-point correlation function slow the free boson , lambast the electric potential energy mid two unit charges in figure dimensions.[3]