An intrinsic curvature model is investigated using the canonical Monte Carlosimulations on dynamically triangulated spherical surfaces of size upto N=4842with two fixed-vertices separated by the distance 2L. We found a first-ordertransition at finite curvature coefficient \alpha, and moreover that the orderof the transition remains unchanged even when L is enlarged such that thesurfaces become sufficiently oblong. This is in sharp contrast to the knownresults of the same model on tethered surfaces, where the transition weakens toa second-order one as L is increased. The phase transition of the model in thispaper separates the smooth phase from the crumpled phase. The surfaces becomestring-like between two point-boundaries in the crumpled phase. On thecontrary, we can see a spherical lump on the oblong surfaces in the smoothphase. The string tension was calculated and was found to have a jump at thetransition point. The value of \sigma is independent of L in the smooth phase,while it increases with increasing L in the crumpled phase. This behavior of\sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu,where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpledphase. We should note that a possibility of a continuous transition is notcompletely eliminated.
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