ISSN:
1572-9613
Keywords:
Spherical model
;
Coulombic systems
;
correlation function decay
;
Stillinger-Lovett relations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider simple cubic lattice systemsΛ ind dimensions with a continuous real charge variableq(n) at each lattice siten. These variables are subject t'o a mean spherical constraint forcing 〈∑n∈Λ q 2(n)〉=‖Λ‖Q 2, where ‖Λ‖ is the number of lattice sites inΛ andQ is an elementary charge. The energy of the charges comes from interactions with an electrostatic potential, which is the solution of a symmetric second-difference Poisson equation on the lattice. Two cases are considered, both of which allow the inclusion of the effects of a fixed, constant, external electric field. On the latticeΛ 1=[1,N]⊗d , a Neumann condition is imposed at the surface of the lattice. The latticeΛ 2=[1,N]⊗ [−M,M]⊗(d−1) is periodic in each direction ranging over [−M, M] and has a Dirichlet condition imposed at the other two surfaces. OnΛ 2 a finite electric field may be applied, while onΛ 2 a finite potential difference may be applied across the lattice. The models are exactly solvable. We study the distribution functions on each system and show that they satisfy appropriate forms of the first two Stillinger-Lovett moment conditions. The two charge distribution functions show screening behavior at high temperature and extreme short range at an intermediate temperatureT 0(d), and oscillate as they decay to zero forT〈T 0(d). Because of the continuous nature of the charge variables, there is no Kosterlitz-Thouless transition in two dimensions. In three dimensions the change in the decay behavior of the distribution functions atT〈T 0(d) is precursor to a phase transition to a charge ordered state.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01026501
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