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

TL;DR

This paper investigates the thermodynamic properties of Ising spins on the triangular kagome lattice using exact analytical methods and Monte Carlo simulations, revealing complex phase behavior and spin liquid states.

Contribution

It provides the first comprehensive analysis combining exact solutions and simulations for this lattice, detailing phase diagrams and residual entropies.

Findings

Ground state is a spin liquid with residual entropy ~0.4752.

Weak magnetic field induces a dimer model with irrational residual entropy.

Power-law spin correlations transition to exponential decay at finite temperatures.

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 $s_0/k_B={1/9} \ln 72\approx 0.4752...$. 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.