Emergent Berezinskii-Kosterlitz-Thouless deconfinement in super-Coulombic plasmas

TL;DR

This work demonstrates that two-dimensional gases with super-Coulombic power-law interactions exhibit a finite-temperature Berezinskii-Kosterlitz-Thouless confinement–deconfinement transition, driven by dielectric screening that induces an emergent Coulomb interaction at long distances. Using numerically exact Monte Carlo simulations and a test-charge based method to extract the effective potential, the authors show a universal jump in the long-wavelength Coulomb coupling, $\kappa_\infty = 4 T_c$, persisting across a range of power laws $\sigma$ and densities $\rho$. They identify a crossover lengthscale $\xi_c$ signaling the onset of the emergent Coulomb regime and confirm that the true Coulomb description and BKT criticality survive under finite-size scaling, with phase boundaries obeying $\kappa = 4 T$ at $T_c$. The results generalize BKT physics to generic long-range interactions, validate dielectric-screening predictions, and provide a robust test-charge framework to probe emergent interactions in complex media. This has broad implications for 2D systems with long-range interactions and supports the universality of Coulomb emergence in super-Coulombic gases.

Abstract

We study the statistical mechanics of two-dimensional "super-Coulombic" plasmas, namely, neutral plasmas with power-law interactions longer-ranged than Coulomb. To that end, we employ numerically exact large-scale Monte Carlo simulations. Contrary to naive energy-entropy arguments, we observe a charge confinement-deconfinement transition as a function of temperature. Remarkably, the transition lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. Our results corroborate recent dielectric medium and renormalization group calculations predicting effective long-scale Coulomb interactions in microscopically super-Coulombic gases. We explicitly showcase this novel dielectric screening phenomenon, capturing the emergent Coulomb potential and the associated crossover length scale. This is achieved by utilizing a new test charge based methodology for determining effective inter-particle interactions. Lastly, we show that this Coulomb emergence and the associated BKT transition occur universally across generic interactions and densities.

Figures (15)

• Figure 1: Monte Carlo snapshots of a super-Coulombic gas with confining power-law, $r^\sigma$, interaction, with $\sigma=0.25$ and particle density $\rho=0.01$ in its (a) confined and (b) deconfined phases separated by a BKT phase transition. The orange (blue) circles indicate positive (negative) charges. (c) The power law vs temperature phase diagram for fixed particle density $\rho=0.01$. (d) The particle density vs temperature phase diagram for fixed power law $\sigma=0.25$. The red points indicate BKT critical points observed using our simulations; the phase boundary is constructed by interpolating between them.
• Figure 2: (a) The effective test charge potential for a $\sigma=0.25$, $\rho=0.01$, super-Coulombic gas at $T=0.075$, showcasing the crossover from its bare $r^\sigma$ potential to an emergent Coulomb-like logarithmic form. (b) The effective potential for the same gas at different confining temperatures, contrasted against the bare interaction.
• Figure 3: (a) The Coulomb coupling vs temperature for a $\sigma=0.25$, $\rho=0.01$ super-Coulombic gas showcasing deconfinement. The dashed line represents the universal $\kappa=4T$ BKT line. (b) The universal BKT scaling function for $\kappa_{L}/T$ vs $L/\xi$ in the vicinity of $T>T_{\text{BKT}}$ for the same gas with activated scaling $\xi \sim \exp(b/\sqrt{T-T_{\text{BKT}}})$. Note that since $\rho$ is fixed, $L\sim \sqrt{N}$.
• Figure 4: (a) Finite size scaling of the effective Coulomb coupling for different temperatures in the confined phase. The dashed lines represent extrapolation to the thermodynamic limit, showcasing convergence to finite constants. (b) Schematic depiction of the temperature dependence of the thermodynamic Coulomb couplings for a microscopically Coulomb gas with bare coupling $\kappa_{0}$ and an arbitrary microscopically super-Coulombic gas.
• Figure 5: The Coulomb coupling for different system sizes showcasing the BKT transition by varying (a) the power law $\sigma$, and (b) the particle density $\rho$. Both plots are for a fixed temperature $T=0.078$. The dashed horizontal lines show the critical value $\kappa=4T_{\text{BKT}}\sim 4\times0.078$.