Spin correlation function in 2D statistical mechanics models with inhomogeneous line defects

TL;DR

This paper derives an analytical expression for the critical spin-spin correlation function in a 2D Ising model with an arbitrary inhomogeneous line defect, illustrating the transition from scaling to non-scaling behavior.

Contribution

It provides one of the few analytical solutions for a 2D critical system with inhomogeneous defects, extending the understanding of non-uniform perturbations.

Findings

The spin correlator exhibits a transition from scaling to non-scaling behavior.

Non-scaling behavior persists in the Ashkin-Teller model with similar defects.

Analytical expression derived using path-integral techniques in fermionic continuum description.

Abstract

We consider the critical spin-spin correlation function of the 2D Ising model with a line defect which strength is an arbitrary function of position. By using path-integral techniques in the continuum description of this model in terms of fermion fields, we obtain an analytical expression for the correlator as functional of the position dependent coupling. Thus, our result provides one of the few analytical examples that allows to illustrate the transit of a magnetic system from scaling to non-scaling behavior in a critical regime. We also show that the non-scaling behavior obtained for the spin correlator along a non-uniformly altered line of an Ising model remains unchanged in the Ashkin-Teller model.