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Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas

K. Borkje·S. Kragset·A. Sudbo
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Abstract

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D XY model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.

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K. Borkje, S. Kragset, A. Sudbo. 2004-12-10. Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas. https://doi.org/10.1103/physrevb.71.085112

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