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.

arXiv comment15 pages, 16 figures, published version (http://www.physics.purdue.edu/~dyao/)

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• Ising models of quantum frustration
• Enhanced magnetocaloric effect in frustrated magnets
• Two-dimensional periodic frustrated Ising models in a transverse field
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Theory of the [111] magnetization plateau in spin ice
• Finite low-temperature entropy of some strongly frustrated quantum spin lattices in the vicinity of the saturation field
• Magnetization process of spin ice in a [111] magnetic field
• Pocket Monte Carlo algorithm for classical doped dimer models
• Correlations and confinement in non-planar two-dimensional dimer models
• "Exact" Algorithm for Random-Bond Ising Models in 2D
• Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

Cited by in corpus (26)

• Kondo Metal and Ferrimagnetic Insulator on the Triangular Kagomé Lattice
• 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
• Direct algebraic mapping transformation for decorated spin models
• Frustrated Ising model on the Cairo pentagonal lattice
• Topological magnons on the triangular kagome lattice
• Unconventional quantum ordered and disordered states in the highly frustrated spin-1/2 Ising-Heisenberg model on triangles-in-triangles lattices
• Spin glass induced by infinitesimal disorder in geometrically frustrated kagome lattice
• Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings
• Dimers on the Triangular Kagome Lattice
• Localized states on triangular traps and low-temperature properties of the antiferromagnetic Heisenberg and repulsive Hubbard models
• Coexistence of spin-1 fermion and Dirac fermion 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
• Geometrically frustrated Ising-Heisenberg spin model on expanded Kagomé lattice
• The antiferromagnetic Ising model on the swedenborgite lattice
• Order-from-disorder effect in the exactly solved mixed spin-(1/2, 1) Ising model on fully frustrated triangles-in-triangles lattices
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• The 3-edge-colouring problem on the 4-8 and 3-12 lattices
• Dynamic approach to finite-temperature magnetic phase transitions in the extended J1- J2 model with vacancy order
• Magnetocaloric properties of an Ising antiferromagnet on a kagome lattice
• Quantum decoration transformation for spin models
• XXZ-Ising model on the triangular kagome lattice with spin-1 on the decorated trimers
• The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems
• Small-Network Approximations for Geometrically Frustrated Ising Systems
• Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice