Single-molecule magnetism originates from the strong intra-moleculer magnetic coupling of a small number of interacting spins. Such spins generally interact very weakly with the neighbouring spins in the other molecules of the compound, therefore, inter-molecular spin couplings are negligible. In certain cases the number of magnetically coupled spins is as small as a dimer, a system that can be considered the smallest nanomagnet capable of storing non-trivial magnetic information on the molecular level. Additional interesting patterns arise if the spin motion is confined to a two-dimensional space. In such a scenario, clusters consisting of spins with large-spin values are particularly attractive since their magnetic interactions can be described well in terms of classical Heisenberg XY spins. In this work we calculate exactly the magnetic properties of a nanomagnetic dimer of classical XY spins in a "planar" external magnetic field. The problem is solved by employing a mathematical approach whose idea is the introduction of auxiliary spin variables into the starting expression of the partition function. Results for the total internal energy, total magnetic moment, spin-spin correlation function and zero-field magnetic susceptibility can serve as a basis to understand the magnetic properties of large-spin dimer building blocks.
In this article, we discuss general properties of the q-opinion model which is based on the extension of the XY magnet model. After considering a short briefing of our recently introduced q-XY model and providing the general statistical mechanics calculation for it, we analyzed specifics and application for the of the 2-node chain. The model is capable to interpret some particular features of the opinion in a couple including shifting behavior, losing interest on a given issue for specific opinion microstates etc. We proposed to use this model in a manded version of the preferential attachment rule for link establishment in a social network. Doi: 10.28991/HEF-2020-01-02-05 Full Text: PDF
In this work we have studied the spreading of militantism in 1D and 2D square lattice by operating the q-XY opinion and its utility optimization as control mechanism for the update process. The average utility and opinion value for a pair of opinion nodes are calculated in the framework of standard statistical mechanics using the q-opinion utility U = − J 2 ( O → 2 − 2 ) − F O → + q ( J 2 ( O → 2 − 2 ) ∗ F O → ) . The agreement with an incoming zealot opinion is modelled as one by one dialogue starting from a random opinion configuration. Each time step one node updates its opinion value according to a set of rules and by specific probabilities based on local utility improvement. New opinion values are accepted with a Metropolis-like probability calculated by employing q-utilities of the nodes under updating process. For the chain opinion structure in the interaction type preserving regimes where 1 − q J 2 ( O → 2 − 2 ) > 0 given 0 ≤ O ≤ 1 it resulted that that both 1D and 2D structures accept the militant offer only partially. For bounded chain the agreement level is at average values for short chain and low values for bounded long opinion chain. Bounded chain structures are found resistant toward militantism accommodation. For square opinion lattices we obtained also that the militant attitude would never cover all the community. Homogenous-nodes group resulted somewhat deterring in accepting the militant opinion with an agreement level of around 0.6. For heterogonous communities the edge agreement level closed up to around 0.7-0.8. The model reproduces the fact that there would be always a fraction of opposition whatsoever regime is applied. It produces various outcomes imitating the complexity of the social behaviour.
The presence of heavy metals in the maritime waters has been constantly considered as an important issue in the environmental aspects. In this framework, herein we report some findings from measurements of concentration of so called heavy metals in the sea waters of the Vlora (Albania). We obtained that the concentrations of Cu. Fe, Cd, Mn, are in the range of their average values in other Adriatic places. Usually the concentration of those elements depends on the positions where measurement have been made, indicating that isolated sources of pollution are
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