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Magnetic and magnetocaloric properties of geometrically frustrated antiferromagnetic Ising (IA) and ferromagnetic spin ice (SI) models on a nanocluster with a ‘Star of David’ topology, including next-nearest-neighbor (NNN) interactions, are studied by an exact enumeration. In an external field applied in characteristic directions of the respective models, depending on the NNN interaction sign and magnitude, the ground state magnetization of the IA model is found to display up to three intermediate plateaus at fractional values of the saturation magnetization, while the SI model shows only one zero-magnetization plateau and only for the antiferromagnetic NNN coupling. A giant magnetocaloric effect is revealed in the IA model with the NNN interaction either absent or equal to the nearest-neighbor coupling. The latter is characterized by abrupt isothermal entropy changes at low temperatures and infinitely fast adiabatic temperature variations for specific entropy values in the processes when the magnetic field either vanishes or tends to the critical values related to the magnetization jumps. [ABSTRACT FROM AUTHOR]

• We study a frustrated general spin-S Ising antiferromagnet on a kagome lattice. • We explore possibility of long-range ordering for any finite or infinite values of S. • Character of the spin-correlation function is studied by Monte Carlo simulations. • It is found that system remains disordered for any spin S and any finite temperature. The possibility of the emergence of some kind of long-range ordering (LRO) due to the increase of multiplicity of the local degrees of freedom (spin value S) is studied in an Ising antiferromagnet on a kagome lattice (IAKL) by Monte Carlo simulation. In particular, the critical exponent of the spin correlation function, obtained from a finite-size scaling analysis, is evaluated for various values of S , including S = ∞ , with the goal to determine whether there exists some threshold value of the spin S C above which the system would show true or quasi-LRO, similar to a related model on a triangular lattice (IATL). It is found that, unlike in the IATL case, the IAKL model remains disordered for any spin value and any finite temperature. [ABSTRACT FROM AUTHOR]