Classical Spin Liquid Properties of the Infinite-Component Spin Vector Model on a Fully Frustrated Two Dimensional Lattice

Abstract

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, $D\to \infty$. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, $r\lesssim {\xi }_c\propto \exp (T^{\ast }/T)$, correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as $<{\mathbf{S}}_0{\mathbf{S}}_r>\propto 1/r^2$ in the range $a_0\ll r\ll {\xi }_c\propto T^{-1/2}$, where $a_0$ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D=3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid.

9 pages (epj-style, two columns), 7 figures. Version to be published in EPJ B

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• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Multi-$Q$ magnetic phases from frustration and chiral interactions
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Anisotropic Spin Ice on a Breathing Pyrochlore Lattice