MSc defence "Phase Transitions in Cities -- Modelling Land Use Interactions on a 2d Ising Lattice"

by Mr Justus Heuer (TPI)

Monday 30 Sept 2024, 15:00 → 17:00 Europe/Berlin

SR 102 (TPI, FSU Jena)

Cities are complex systems with a multitude of interactions between individuals and infrastructures shaping the patterns of buildings on a macroscopic level. The origin of their characteristic behavior is often not well understood. Lattice models from statistical physics provide a mathematical framework for the stochastic analysis of such patterns forming from simple microscopic interactions between large sets of individual data points. This thesis uses a multi-layer two-dimensional Ising model approach with a Hamiltonian that describes the interaction between different building types to calculate key observables such as the average shares, critical exponents, and characteristic pattern sizes of these building types. The calculations are performed using methods from renormalization group theory, mean-field theory, and Monte Carlo simulations, and the results are subsequently tested with data on building shares in different Californian counties and on building patterns in New York City. The comparison of the theoretical model and the data analysis indicates that interaction-based Ising-like models with Boltzmann probability distributions in the critical region around the phase transition are generally suitable to replicate the behavior of existing cities. Also, the results of the Monte Carlo simulations of the model suggest that it might show multicritical behavior in a subsystem with two separate phase transitions.