Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

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.

arXiv comment26 pages, 9 figures, published version

References in corpus (4)

• Spatially Anisotropic Heisenberg Kagome Antiferromagnet
• Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite
• Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite
• Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagomé lattice

Cited by in corpus (4)

• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings
• Reentrance of disorder in the anisotropic shuriken Ising model
• Berezinskii-Kosterlitz-Thouless phase transitions of the antiferromagnetic Ising model with ferromagnetic next-nearest-neighbor interactions on the kagome lattice