The Ising model S = 1/2 and the S = 1 model are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well known 2d Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S = 1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2d Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S = 1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.

In this study, by means of classical molecular dynamics simulations, we investigated the thermal transport properties of hexagonal single-layer, zinc-blend and wurtzite phases of BN, AlN, and GaN crystals, which are very promising for the application and design of high-quality electronic devices. With this in mind, we generated fully transferable Tersoff-type empirical inter-atomic potential parameter sets by utilizing an optimization procedure based on particle swarm optimization. The predicted thermal properties as well as the structural, mechanical and vibrational properties of all materials are in very good agreement with existing experimental and first-principles data. The impact of isotopes on thermal transport is also investigated and between ∼10 and 50% reduction in phonon thermal transport with random isotope distribution is observed in BN and GaN crystals. Our investigation distinctly shows that the generated parameter sets are fully transferable and very useful in exploring the thermal properties of systems containing these nitrides.

The structure and thermal boundary conductance of the wurtzite GaN/AlN (0001) interface are investigated using molecular dynamics simulation. Simulation results with three different empirical interatomic potentials have produced similar misfit dislocation networks and dislocation core structures. Specifically, the misfit dislocation network at the GaN/AlN interface is found to consist of pure edge dislocations with a Burgers vector of 1/3⟨12¯10⟩ and the misfit dislocation core has an eight-atom ring structure. Although different interatomic potentials lead to different dislocation properties and thermal conductance values, all have demonstrated a significant effect of misfit dislocations on the thermal boundary conductance of the GaN/AlN (0001) interface.

Direct experimental measurement of thermal expansion coefficient without substrate effects is a challenging task for two-dimensional (2D) materials, and its accurate estimation with large-scale ab initio molecular dynamics is computationally very expensive. Machine learning-based interatomic potentials trained with ab initio data have been successfully used in molecular dynamics simulations to decrease the computational cost without compromising the accuracy. In this study, we investigated using Gaussian approximation potentials to reproduce the density functional theory-level accuracy for graphene within both lattice dynamical and molecular dynamical methods, and to extend their applicability to larger length and time scales. Two such potentials are considered, GAP17 and GAP20. GAP17, which was trained with pristine graphene structures, is found to give closer results to density functional theory calculations at different scales. Further vibrational and structural analyses verify that the same conclusions can be deduced with density functional theory level in terms of the reasoning of the thermal expansion behavior, and the negative thermal expansion behavior is associated with long-range out-of-plane phonon vibrations. Thus, it is argued that the enabled larger system sizes by machine learning potentials may even enhance the accuracy compared to small-size-limited ab initio molecular dynamics.

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