The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the \(O(N)\) models from \(N=1\) (Ising model) to \(N=0\) (polymer). The unitarity bound below \(N=1\) of the scaling dimension for the the \(O(N)\)-symmetric-tensor develops a kink as a function of the fundamental field as in the case of the energy operator dimension in the Ising model. Although this kink structure becomes less pronounced as \(N\) tends to zero, an emerging asymmetric minimum in the current central charge \(C_J\) can be used to locate the CFT. It is pointed out that certain level degeneracies at the \(O(N)\) CFT should induce these singular shapes of the unitarity bounds. As an application to the quantum and classical spin systems, we also predict critical exponents associated with the \(\mathcal{N}=1\) supersymmetry, which could be useful for numerically locating the tricritical point in the phase diagram.