We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a ballistic phase, an adsorbed phase and a mixed phase where part of the 3-star is adsorbed and part is ballistic. We use both rigorous arguments and Monte Carlo methods to map out the phase diagram, and investigate the location and nature of the phase transition boundaries. In two dimensions, only two of the arms can be fully adsorbed in the surface and this alters the phase diagram when compared to 3-stars in three dimensions.
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