2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156604We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the scaling behavior of the surface magnetization, and the energy of a soft mode. All three lead to a log-normal distribution of the pseudo-critical transverse fields, where the width scales as $L^{-1/ν}$ with $ν=2$ and the shift of the average value scales as $L^{-1/ν_{typ}}$ with $ν_{typ}=1$, which we related to the scaling of average and typical quantities in the critical region.4 pages, 2 figuresDisordered Systems and Neural NetworksStatistical Mechanicstext