Phase transitions in normal mode spectra of two-dimensional clusters in an anisotropic power-law confining potential

On the convergence issues of the block‐average method for the melting of two‐dimensional confined systems

“…[8] First, an orientational melting occurs (first peak), followed by the total melting which takes place at higher temperature (second peak). One can say that the configuration (3,16) is less stable than the configuration (1,6,12), and this is in agreement with the first-principles results of the normal mode analysis (see Section 3).…”

“…For the Coulomb cluster = 0, the highest LNF is obtained in the case of a parabolic trap with √ 2 min ∕ 0 = 0.667. This means that the configuration (1, 6, 12) is more stable than the hard-wall configuration (3,16) in which the LNF is close to zero. In other words, normal mode analysis expects a high melting temperature for well-packed configurations.…”

“…Figure 1a displays the simulated ground-state configurations of a 19-particle Coulomb cluster ( = 0) in both parabolic (n = 2) and hard-wall traps. It is clear that the former structure results in a well-packed configuration (1,6,12), whereas the later one is not well packed (3,16).…”

“…During the past few decades, several models and criteria have been tested to understand the phenomenon of the melting phase transition in 2D and 3D few‐particle systems in traps. The interest behind these studies originates from the tendency to control pattern formation in different physical environments, including plasmas, semiconductors, and superconductor materials, where small structures (clusters) find significant experimental realizations.…”

“…Results for a non-well-packed configuration(3,16). (Left): Block-averaged variance as a function of block size; (right): temperature dependence of VIDF process, i.e.…”