  The "melting" of self-formed rigid structures made of a small number of
interacting classical particles confined in an irregular two-dimensional space
is investigated using Monte Carlo simulations. It is shown that the interplay
of long-range Coulomb repulsions between these particles and the irregular
confinement yields a solid-like phase at low temperatures that possesses a
bond-orientational order, however, the positional order is depleted even at the
lowest temperatures. Upon including thermal fluctuations, this solid-like phase
smoothly crosses over to a liquid-like phase by destroying the
bond-orientational order. The collapse of solidity is shown to be defect
mediated, and aided by the proliferation of free disclinations. The behavior of
different physical observables across the crossover region are obtained. Our
results will help quantifying melting found in experiments on systems with
confined geometries.
