Magnetization processes and phase transitions in a geometrically frustrated triangular lattice Ising antiferromagnet in the presence of an external magnetic field and a random site dilution are studied by the use of an effective-field theory with correlations. We find that the interplay between the applied field and the frustration-relieving dilution results in peculiar phase diagrams in the temperaturefield-dilution parameter space.

We study the critical behavior of a frustrated Blume-Capel (BC) antiferromagnet on a triangular lattice by Monte Carlo simulations. For a reduced single-ion anisotropy strength −1.47 d < 0 we find two phase transitions. The low-temperature phase is characterized by the antiferromagnetic long-range ordering (LRO) on two sublattices with the third one remaining in a non-magnetic state.

Thermodynamic and magnetocaloric properties of geometrically frustrated Ising spin clusters of selected shapes and sizes are studied by exact enumeration. In the ground state the magnetization and the entropy show step-wise variations with an applied magnetic field. The number of steps, their widths and heights depend on the cluster shape and size. While the character of the magnetization plateau heights is always increasing, the entropy is not necessarily decreasing function of the field, as one would expect. For selected clusters showing some interesting ground-state properties, the calculations are extended to finite temperatures by exact enumeration of densities of states in the energy-magnetization space. In zero field the focus is laid on a peculiar behavior of some thermodynamic quantities, such as the entropy, the specific heat and the magnetic susceptibility. In finite fields various thermodynamic functions are studied in the temperature-field parameter plane and particular attention is paid to the cases showing an enhanced magnetocaloric effect. The exact results on the finite clusters are compared with the thermodynamic limit behavior obtained from Monte Carlo simulations.

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- (J1<0) and second-nearest-neighbor (J2<0) interactions are studied within the framework of the effective-field theory with correlations based on the different cluster sizes and for a wide range of R=J2/|J1|. Despite the simplicity of the model, it has proved difficult to precisely determine the order of the phase transitions. In contrast to the previous effective-field study, we have found a first-order transition line in the region close to R=-0.5 not only between the superantiferromagnetic and paramagnetic (R<-0.5) but also between antiferromagnetic and paramagnetic (R>-0.5) phases.

Ground state phases of a generalized XY model with magnetic and generalized nematic couplings on a non-bipartite triangular lattice are investigated in the exchange interactions parameter space. We demonstrate that the model displays a number of ordered and quasi-ordered phases as a result of geometrical frustration and/or competition between the magnetic and generalized nematic interactions. The nature and the extent of the respective phases depend on the parameter q, characterizing the higher-order harmonics term in the Hamiltonian. Motivated by the recent discovery of the experimental realization of the model with q = 2 in the seemingly unrelated field of the systems chemistry [A.B. Cairns et al., Nature Chemistry 8, 442 (2016)], the model for q > 2 is discussed in the context of the prediction of structural phases of a class of bimetalic cyanides based on a mapping between the two systems.

a b s t r a c tBy means of standard and histogram Monte Carlo simulations, we investigate the critical and compensation behaviour of a ternary mixed spin alloy of the type AB p C 1 À p on a cubic lattice. We focus on the case with the parameters corresponding to the Prussian blue analog ðNi II p Mn II 1Àp Þ 1:5 ½Cr III ðCNÞ 6 Á nH 2 O and confront our findings with those obtained by some approximative approaches and the experiments.

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We use the effective-field theory with correlations based on different cluster sizes to investigate phase diagrams of the frustrated Ising antiferromagnet on the honeycomb lattice with isotropic interactions of the strength J 1 < 0 between nearestneighbour pairs and J 2 < 0 between next-nearest neighbour pairs of spins. We present results for the ground-state energy as a function of the frustration parameter R = J 2 /|J 1 |. We find that the cluster-size has a considerable effect on the existence and location of a tricritical point in the phase diagram at which the phase transition changes from the second order to the first one.