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Using Monte Carlo simulation we have investigated a classical twodimensional XYmodel with a modified form of interaction which makes the potential well sharper than that in the conventional XYmodel. The conventional XYmodel is known to exhibit a defectmediated continuous phase transition while the modified XYmodel has a strong first order phase transition, both transitions being temperature driven. Performance and relative assessment of WangLandau (WL) algorithm in these class of models have been discussed. Difficulties faced in simulating relatively large continuous systems using WL algorithm have been investigated. Besides applying the cluster algorithm of Wolff, we have used FerrenbergSwendsen multiple histogram reweighting technique and finite size scaling rules of Lee and Kosterlitz. We have also investigated the role played by the topological defects and the factors which are responsible for the change over the nature of the phase transition from a continuous one to a strongly first order one. We have also presented a detailed study of the effect of suppression of topological defects on various physical quantities relevant to this model.
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