Quantum phase transition from magnetic to topological order

We present a numerical study of the quantum phase transition from the magnetically ordered phase to the topologically ordered phase of a $n$-spins $1/2$ system. We show that the derivative of von Neumann entropy of a plaquette diverges at the critical point, signaling a second order quantum phase transition. Moreover, we compute the finite-size scaling of the Topological Entropy, showing how this quantity detects the passage to the topologically ordered phase.