Abstract
A new energy-based chaining criterion was introduced in dipolar systems based on an earlier article by the author, in which the probability of chaining for adjacent particles in a new formula of magnetic susceptibility was used. The probability of chaining and the magnitude of the energy criterion can be calculated from the Monte Carlo (MC) simulation values of magnetic susceptibility. The energy criterion also depends on the dipole moment and the density. At high densities, the energy criterion is well below 70-75%. In addition, it was confirmed by simulation results that the chain length distribution follows a geometric distribution. How the probability of chaining depends on the energy criterion was given empirically and two parameters were fitted to it.
Highlights
According to the literature, the criterion of chaining in dipolar systems is unclear
An energy criterion is used to decide whether two adjacent particles form part of a chain
The energy criterion defines the limit at a certain level of interaction energy between them, which is usually 70 − 75% of the minimum pair interaction energy [1,2,3,4]
Summary
The criterion of chaining in dipolar systems is unclear. The author examined [7] the probability density function of pair interaction energies in a dipolar hard sphere (DHS) system and found that no unit jump-like change in the frequency of the pair interaction energy would justify the introduction of a general criterion based on the pair interaction energy Such a general definition does not take into account the effect of density, while it can be assumed that chaining occurs at different densities and different energy levels of the same dipole moments. The structure of the results is as follows: firstly, through several examples, it is shown that for any energy criterion, the number of chains follows a geometric distribution; secondly, the p values calculated from the magnetic susceptibility values are given; thirdly, from simulations, the Ulim values are determined that provide the desired p value at a given density and dipole moment; by fitting, an empirical formula is derived to describe the relationship p − Ulim
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