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A self-organized system composed of classical particles confined in atwo-dimensional parabolic trap and interacting through a potential with ashort-range attractive part and long-range repulsive part is studied asfunction of temperature. The influence of the competition between theshort-range attractive part of the inter-particle potential and its long-rangerepulsive part on the melting temperature is studied. Different behaviors ofthe melting temperature are found depending on the screening length ($\kappa$)and the strength ($B$) of the attractive part of the inter-particle potential.A re-entrant behavior and a thermal induced phase transition is observed in asmall region of ($\kappa,B$)-space. A structural hysteresis effect is observedas a function of temperature and physically understood as due to the presenceof a potential barrier between different configurations of the system.

Hysteresis and re-entrant melting of a self-organized system of classical particles confined in a parabolic trap