Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

TL;DR

This paper analyzes the correlation functions of the anisotropic kagome lattice Ising antiferromagnet, revealing a disorder line that separates regions with different magnetic behaviors and providing exact and numerical results.

Contribution

It provides a rigorous analytic and numerical study of correlation functions, identifying a disorder line and characterizing phase behavior in the anisotropic kagome Ising antiferromagnet.

Findings

Correlation function vanishes on a specific line J_d(T) in the phase diagram.

Below J_d(T), the system behaves like an unfrustrated 2D Ising model.

Above J_d(T), correlations are influenced by short-range antiferromagnetic order.

Abstract

We study the correlation function of middle spins, i. e. of spins on intermediate sites between two adjacent parallel lattice axes, of the spatially anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously by a Toeplitz determinant. The large-distance behaviour of this correlation function is obtained by analytic methods. For shorter distances we evaluate the Toeplitz determinant numerically. The correlation function is found to vanish exactly on a line J_d(T) in the T-J (temperature vs. coupling constant) phase diagram. This disorder line divides the phase diagram into two regions. For J less than J_d(T) the correlations display the features of an unfrustrated two-dimensional Ising magnet, whereas for J greater than J_d(T) the correlations between the middle spins are seen to be strongly influenced by the short-range antiferromagnetic order that prevails among the spins of the adjacent lattice axes. While for J less than J_d(T) there is a region with ferrimagnetic long-range order, the model remains disordered for J greater than J_d(T) down to T=0.