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At this transition in $2d$ its fractal dimension is $1.750\\pm 0.003$, and one obtains a novel set of critical exponents $\\beta_{eb} = 0.50\\pm 0.02$, $\\gamma_{eb} = 1.97\\pm 0.05$, and $\\nu_{eb} = 2.00\\pm 0.02$ fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. 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Moreira, Cesar I. N. Sampaio Filho, Hans J. Herrmann, Jos\\'e S. Andrade Jr.","submitted_at":"2018-03-21T12:19:49Z","abstract_excerpt":"The elastic backbone is the set of all shortest paths. We found a new phase transition at $p_{eb}$ above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in $2d$ its fractal dimension is $1.750\\pm 0.003$, and one obtains a novel set of critical exponents $\\beta_{eb} = 0.50\\pm 0.02$, $\\gamma_{eb} = 1.97\\pm 0.05$, and $\\nu_{eb} = 2.00\\pm 0.02$ fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. 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