Seminarium Fizyki Materii Skondensowanej

We fill a void in merging empirical and phenomenological characterisationof the dynamical phase transitions in complex systems by identifyingthree, essentially different, dynamical phase transitions on real-lifefinancial markets driven by `macrodynamics' of a superstar-like superhub.We collect and interpret the empirical, numerical, and semi-analyticalevidences for the existence of these phase transtions, by considering theFrankfurt Stock Exchange (FSE), as a typical example of a financial marketof a medium size. Using the canonical object for the graph theory, i.e.the Minimal Spanning Tree (MST) network, we observe: (i) The initial phasetransition from the equilibrium to non-equilibrium MST network in itsnucleation phase, occuring at some critical time 2005-08-11 (Thursday).Coalescence of edges on the FSE's transient leader SALZGITTER (SZG)AG-Stahl und Technologie company, is observed within the nucleation and isapproximately characterised by the Lifsthiz-Slyozov growth exponent; (ii)The nucleation accelerates and transforms to the condensation process, inthe second phase transition, forming a logarithmically diverging λ-peak ofshort-range order parameters at the subsequent critical time 2007-01-25(Thursday); (iii) In the third phase transition, the peak logarithmicallydecreases over three quarters of the year, resulting in a few looslyconnected sub-graphs. The λ-peak, resembling the continuous phasetransition from the normal fluid I 4He to the superfluid II 4He isreminiscent of a non-equilibrium superstar-like superhub, or a `dragonking', abruptly accelerating the evolution of the SZG company. All thesephase transitions are caused by the few richest vertices, which drifttowards the SZG centre, providing most of the edges. Thanks to thelocation of these richest vertices in the first, second or thirdcoordination layers, the SZG vertex unusually increases its own degree.Thus, we capture an amazing phenomenon, likely of a more universalcharacter, where a periferial vertex becomes the one which isoverdominating the complex network during an exceptionally long period oftime. However, to directly relate all these phenomena to the rulesdefining the algorithm for constructing evolving MST networks, stillremains a challenge.