Cooperative behaviour in complex systems

TL;DR

This thesis explores cooperative phenomena in complex systems through statistical physics, analyzing phase transitions, critical behavior, and universal features across various models and network structures.

Contribution

It provides new insights into non-equilibrium phase transitions, critical densities, and dynamical behaviors in complex network and lattice models.

Findings

Non-equilibrium phase transitions in weighted scale-free networks

Critical cluster densities in conformal invariant systems

Dynamical behavior of antiferromagnetic Ising model at criticality

Abstract

In my PhD thesis I studied cooperative phenomena arise in complex systems using the methods of statistical and computational physics. The aim of my work was also to study the critical behaviour of interacting many-body systems during their phase transitions and describe their universal features analytically and by means of numerical calculations. In order to do so I completed studies in four different subjects. My first investigated subject was a study of non-equilibrium phase transitions in weighted scale-free networks. The second problem I examined was the ferromagnetic random bond Potts model with large values of q on evolving scale-free networks which problem is equivalent to an optimal cooperation problem. The third examined problem was related to the large-q sate random bond Potts model also and I examined the critical density of clusters which touched a certain border of a perpendicular strip like geometry and expected to hold analytical forms deduced from conformal invariance. The last investigated problem was a study of the non-equilibrium dynamical behaviour of the antiferromagnetic Ising model on two-dimensional triangular lattice at zero temperature in the absence of external field and at the Kosterlitz-Thouless phase transition point.