Anomalous scaling dimensions and critical points in type-II superconductors

TL;DR

This paper demonstrates the existence of a stable critical point in the Ginzburg-Landau theory for superconductors, characterized by a negative anomalous dimension of the dual scalar field, indicating a distinct universality class from traditional models.

Contribution

It provides direct Monte Carlo evidence for a new critical point with negative anomalous dimension in the dual description of superconductors, revealing a different universality class.

Findings

Identification of a stable critical point separate from known fixed points.

Negative anomalous dimension of the dual scalar field at the critical point.

Presence of long-range vectorial interactions affecting critical behavior.

Abstract

The existence of a {\it stable critical point}, separate from the Gaussian and XY critical points, of the Ginzburg-Landau theory for superconductors, is demonstrated by direct extraction via Monte-Carlo simulations, of a negative anomalous dimension $\eta_{\phi}$ of a complex scalar field $\phi$ forming a dual description of a neutral superfluid. The dual of the neutral superfluid is isomorphic to a charged superfluid coupled to a massless gauge-field. The anomalous scaling dimension of the superfluid order-field is positive, while we find that the anomalous dimension of the dual field is negative. The dual gauge-field does not decouple from the dual complex matter-field at the critical point. {\it These two critical theories represent separate fixed points.} The physical meaning of a negative $\eta_{\phi}$ is that the vortex-loop tangle of the superfluid at the critical point fills space {\it more} efficiently than random walkers, {\it without collapsing}. This is due to the presence of the massless dual gauge-field, and the resulting long-ranged {\it vectorial} Biot-Savart interaction between vortex-loop segments, which is a relevant perturbation to the steric $|\psi|^4$ repulsion term. Hence, the critical dual theory is not in the universality class of the $|\psi|^4$-theory.