On the size of boundary effects in the Ising chain

We discuss the length at which boundaries affect the magnetization of the quantum Ising chain with free ends. For this purpose we introduce two characteristic length scales describing the size of the boundary-modified region in respectively, longitudinal and transverse magnetization. We show that their finite-size scaling behaviour encodes the position of the critical point and the universal scaling exponent.. The behaviour of proposed lengths in small systems is also discussed. These results should be useful in the context of both numerical and experimental studies.