Casimir effect and deconfinement phase transition

We show that the Casimir effect may lead to a deconfinement phase transition induced by the presence of boundaries in confining gauge theories. Using first-principle numerical simulations we demonstrate this phenomenon in the simplest case of the compact lattice electrodynamics in two spatial dimensions. We find that the critical temperature of the deconfinement transition in the vacuum between two parallel dielectric/metallic wires is a monotonically increasing function of the separation between the wires. At infinite separation the wires do not affect the critical temperature while at small separations the vacuum between the wires loses the confinement property due to modification of vacuum fluctuations of virtual monopoles.

Figure 1

The monopole density in lattice units (20) as the function of the wire strength (13) for various fixed separations between the plates $R$ at the lattice gauge coupling $\beta =0.4$. The error bars are smaller than the size of the markers. The lines are plotted to guide the eyes.

Figure 2

Monopole density in between wires in the perfectly metallic limit $ϵ\to \infty$ as the function of interwire separation $R$ for various fixed gauge couplings $\beta$. Notations are the same as in Fig. 1.

Figure 3

Monopole density in between the plates (the red dots) and outside the plates (the blue dots) as compared to the total density of monopoles on the whole lattice (the green dots) at strong coupling $\beta =0.4$ and the smallest separation between the Casimir wires, $R=a$.

Figure 4

The expectation value of the Polyakov loop in between the plates (25) vs the coupling constant $\beta$ at various values of the excess of the coupling constant $\delta \beta$ at the plates (13) for two fixed separations between the plates, $R=2a$ (top) and $R=5a$ (bottom). The curves correspond to the best fits of the data with the fitting function (27).

Figure 5

The expectation values of the Polyakov loop: in the whole space (24) as well as inside (25) and outside (24) of the wires for a large value of the wire strength $\delta \beta =88$ with the next-to-minimal separation between the wires, $R=2a$.

Figure 6

Pseudocritical coupling constant ${\beta }_c$ of the confinement-deconfinement transition vs the strength of the Casimir plates $\delta \beta$, Eq. (13), for various values of the separation between the plates $R/a=3$, 5, 7, 9. The dashed lines are the fits of the corresponding numerical data by Eq. (29).

Figure 7

Pseudocritical coupling constant ${\beta }_c$ of the confinement-deconfinement transition vs the interwire distance $R$ for the wires in the metallic limit ($\delta \beta \to \infty$ or $ϵ\to \infty$). The line is drawn to guide the eye.

Figure 8

The critical temperature $T_c$ of the confinement-deconfinement transition as the function of the separation between the plates $R$ in the ideal-metal limit ($ϵ\to \infty$) in physical units. The dashed line represents the fit by the function (32) of the numerical data (the red circles).

Figure 9

Phase transition due to the Casimir effect: closely spaced wires (plates) lead to deconfinement of electric charges in the confining phase of compact lattice electrodynamics.