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## 4. Conclusions 

Using Simulated Annealing, a truly three- dimensional approach, we obtain the vortex pat- terns of mesoscopic rods with a point-like mag- netic moment on top. We conclude that rods with thickness smaller than 4 ξ can be considered as thin disks since only top to bottom giant vortex states are obtained. For rods with thickness big- ger than 4 ξ , we observed the appearance of N-fold vortex states, namely N top-to-side vortices. The onset and disappearance of these states is from a single GVS or Meissner state line, as contin- uous transitions from it. Consequently, for suffi- cient large magnetic moments one can retrieve the Meissner state before reaching the normal state, and this, leads to a reentrant behavior. 

## 5. Acknowledgment 

A. R. de C. Romaguera acknowledges the brazilian agency FACEPE for financial support. M. M. Doria acknowledges CNPq and FAPERJ. F. M. Peeters acknowledges Flemish Science Foundation (FWO-Vl), the Belgian Science Pol- icy (IUAP) and the ESF-AQDJJ network. 

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<img src='content_image/436630.jpg'>

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