Thermodynamics of Ising spins on the Triangular Kagome Lattice: Exact analytical method and Monte Carlo simulations

Abstract

We study the thermodynamics of Ising spins on the triangular kagome lattice (TKL) using exact analytic methods as well as Monte Carlo simulations. We present the free energy, internal energy, specific heat, entropy, sublattice magnetizations, and susceptibility. We describe the rich phase diagram of the model as a function of coupling constants, temperature, and applied magnetic field. For frustrated interactions in the absence of applied field, the ground state is a spin liquid phase with integer residual entropy per spin $s_0/k_B=1/9\ln 72\approx \mathrm{0.4752...}$. In weak applied field, the system maps to the dimer model on a honeycomb lattice, with irrational residual entropy 0.0359 per spin and quasi-long-range order with power-law spin-spin correlations that should be detectable by neutron scattering. The power-law correlations become exponential at finite temperatures, but the correlation length may still be long.

15 pages, 16 figures, published version (http://www.physics.purdue.edu/~dyao/)

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• Enhanced magnetocaloric effect in frustrated magnets
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Theory of the [111] magnetization plateau in spin ice
• Magnetization process of spin ice in a [111] magnetic field
• Correlations and confinement in non-planar two-dimensional dimer models
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Cited by in corpus (11)

• Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice
• XXZ and Ising Spins on the Triangular Kagome Lattice
• Topological magnons on the triangular kagome lattice
• Spin glass induced by infinitesimal disorder in geometrically frustrated kagome lattice
• Unconventional quantum ordered and disordered states in the highly frustrated spin-1/2 Ising-Heisenberg model on triangles-in-triangles lattices
• Dimers on the Triangular Kagome Lattice
• Spontaneous order in the highly frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome lattice due to the Dzyaloshinskii-Moriya anisotropy
• Thermodynamic description of the Ising antiferromagnet on triangular lattice with selective dilution by modified Pair Approximation method
• The antiferromagnetic Ising model on the swedenborgite lattice
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice