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Earlier studies of a parametrized class of models, the shortcut models, whose fractal dimension transitions between integer values, indicated that the transition occurs infinitely sharply at the parameter value p = 0, as the system size increases to infinity. In this work, we explain the cause as being due to the combinatorially large increase in the available number of paths connecting a pair of points as the path length is increased. PACS numbers: 05.45.Df, 89.75.HC, 05.50.+q 1

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