Premium
Finite Size Study of the Two‐Dimensional One‐Component Plasma
Author(s) -
Téllez G.
Publication year - 2000
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200007)220:1<769::aid-pssb769>3.0.co;2-q
Subject(s) - physics , dimensionless quantity , coulomb , coupling (piping) , quantum hall effect , quantum mechanics , charge (physics) , inverse , component (thermodynamics) , euler's formula , coupling constant , classical mechanics , mathematical analysis , mathematics , geometry , electron , mechanical engineering , engineering
The two‐dimensional one‐component plasma (2dOCP) is a model in classical statistical mechanics which consists of N mobile point particles of charge q interacting on a surface with a neutralizing background charge density. The dimensionless Coulomb coupling is Γ = β q 2 where β is the inverse temperature. We undertake an exact numerical study into the finite N calculation of the free energy for the 2dOCP both in the disk and the sphere geometries with the coupling constant Γ = 4 and Γ = 6. Due to a formal relationship between the 2dOCP and the quantum Hall effect, in the latter case we used numerical methods previously developed for the study of the Laughlin wave function for fractional filling 1/3. Our results are consistent with the existence of a universal finite‐size correction to the free energy equal to ( χ /12) ln N , where χ denotes the Euler characteristic of the surface, as previously predicted theoretically.