Abstract
We study the high-temperature phase of compact U(1) gauge theory in 2 + 1 dimensions, comparing the results of lattice calculations with analytical predictions from the conformal-field-theory description of the low-temperature phase of the bidimensional XY model. We focus on the two-point correlation functions of probe charges and the field-strength operator, finding excellent quantitative agreement with the functional form and the continuously varying critical indices predicted by conformal field theory.
Highlights
The behavior of U(1) gauge theory at finite temperature T and without matter fields, which has been studied in refs. [54, 87, 91,92,93,94, 101,102,103,104], is interesting: there exists a finite critical temperature Tc such that linear confinement persists for temperatures T < Tc, whereas for T > Tc the potential V associated with a pair of static charges grows logarithmically with their spatial separation r
We focus on the two-point correlation functions of probe charges and the fieldstrength operator, finding excellent quantitative agreement with the functional form and the continuously varying critical indices predicted by conformal field theory
We extend the numerical investigation of the hightemperature phase of the theory to temperatures above Tc: due to the peculiar features of the XY model, which are reviewed 3, universality arguments analogous to those originally discussed in ref. [116] allow one to derive exact analytical predictions for various physical quantities in the high-temperature phase of compact U(1) gauge theory in three dimensions
Summary
The two-dimensional XY model is a statistical model with many important applications in condensed matter systems, such as Josephson-junction arrays [148,149,150], thin layers of superfluid helium [151, 152], planar ferromagnetic materials [153], and the roughening transition [154]. The whole low-temperature phase of the model is characterized by scale-invariant behavior (of Gaußian type), and T = TKT is a multicritical point: this can be shown by generalizing the model with two additional parameters, that control the energy cost of introducing a vortex in the model and the coupling to an explicit symmetry-breaking interaction [120, 161, 162]. The Kosterlitz-Thouless point, at T = TKT, corresponds to K = 2/π, so in the low-temperature phase the scaling dimension of the electric operator s1,0 increases continuously with T as x1,0 = 1/(4πK), tending to the critical value 1/8 — see eq (3.7) – for T → TK−T.
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