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Dr. rer. nat. Sven Lübeck :
Habilitation angenommen durch: Universität
Duisburg-Essen, Campus Duisburg, Fachbereich Physik, 2004-12-10
BetreuerIn: Prof. Dr. K. D. Usadel , Universität
Duisburg-Essen, Campus Duisburg, Fachbereich Physik
GutachterIn: Prof. Dr. K. D. Usadel , Universität
Duisburg-Essen, Campus Duisburg, Fachbereich Physik
Schlüsselwörter in Englisch: phase
transitions, scaling functions, universality
Schlüsselwörter in Deutsch: Skalenfunktion,
Phasenübergang
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Abstrakt in Englisch
Non-equilibrium critical
phenomena have attracted a lot of
research interest in the recent decades. Similar to equilibrium
critical phenomena, the concept of universality remains the major tool
to order the great variety of non-equilibrium phase transitions
systematically. All systems belonging to a given universality class
share the same set of critical exponents, and certain scaling functions
become identical near the critical point. It is known that the scaling
functions vary more widely between different universality classes than
the exponents. Thus, universal scaling functions offer a sensitive and
accurate test for a system's universality class. On the other hand,
universal scaling functions demonstrate the robustness of a given
universality class
impressively. Unfortunately, most studies focus on the determination
of the critical exponents, neglecting the universal
scaling functions. In this work a particular class of non-equilibrium
critical phenomena is considered, the so-called absorbing phase
transitions.
Absorbing phase transitions are expected to occur in physical, chemical
as well as biological systems, and a detailed introduction is
presented. The universal scaling behavior of two different universality
classes is analyzed in detail, namely
the directed percolation and the Manna universality class.
Especially, directed percolation is the most common universality class
of absorbing phase transitions. The presented picture gallery of
universal scaling functions includes steady state, dynamical as well as
finite size scaling functions. In particular, the effect of an external
field conjugated to the order parameter is investigated.
Incorporating the conjugated field, it is possible to determine the
equation of state, the susceptibility, and to perform a modified
finite-size scaling analysis appropriate for absorbing phase
transitions.
Focusing on these equations, the obtained results can be applied to
other non-equilibrium continuous phase transitions observed in
numerical simulations or experiments. Thus, we think that the presented
picture gallery of universal scaling functions is
valuable for future work. Additionally to the manifestation of
universality classes, universal
scaling functions are useful in order to check renormalization group
results quantitatively. Since the renormalization group theory is the
basis of our understanding of critical phenomena, it is of fundamental
interest to examine the accuracy of the obtained results. Due to the
continuing improvement of computer hardware,
accurate numerical data have become available, resulting in a fruitful
interplay between numerical investigations and renormalization group
analyzes.
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