A two-dimensional mesoscopic cluster of "dusty plasma" particles, which can be interpreted as a system of microparticles in an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors are found for clusters of N = 2 -40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as first-order or second-order phase transitions with respect to the parameter R. The disorder ("melting") of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed.
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