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

We present a numerical analysis of several phase transitions which take place in the eigenmode spectrum of a two-dimensional (2D) logarithmic cluster subjected to an anisotropic power law confinement. Varying the anisotropy in a non-parabolic soft confinement drives the system to undergo structural phase transitions of first order, while for a hard wall confinement this variation affects strongly the eigenmode spectrum and breaks the symmetry of the system due to the removal of degeneracy and the coupling between some normal modes.