Phase transitions in "conventional" materials – such as water turning into ice or a metal becoming magnetised – and topological phase transitions have long been treated as fundamentally distinct, governed by different physical principles and lacking a shared conceptual framework. This study, however, published in Physical Review Letters, challenges that notion. Antimo Marrazzo, assistant professor at SISSA, together with Roberta Favata and Nicolas Baù, PhD students at the University of Trieste, have shown that—even in topological phase transitions—certain local markers can exhibit behaviours analogous to those of conventional local order parameters. Just like in a magnet near its critical temperature, these systems exhibit significant local fluctuations. The researchers also identified universal critical exponents, i.e. numerical values that describe how a topological phase transition unfolds and that remain consistent across different materials, as seen in conventional phase transitions. According to the authors, this discovery builds a conceptual bridge between the world of topology and the physics of phase transitions.