Physics Seminar
Title: Kosterlitz-Thouless Transitions in the 1/r2 Ising Chain and Disorder-Modified Colloidal Crystals
Speaker: Owen Tower, Ph.D. Candidate, Brown University
Date: Thursday, April 9, 2026
Time: 12:00pm
Location: SENG 201
Abstract:
We present a series of computational and experimental investigations of systems exhibiting Kosterlitz-Thouless (KT) transitions. Monte Carlo simulations are performed for the 1/r2 Ising model both with and without quenched disorder, and digital microscopy is used together with microfabricated substrates to construct and study two-dimensional colloidal crystals.
For the 1/r2 Ising model, we combine renormalization-group analysis with Monte Carlo simulations to determine the critical temperature of this model and characterize its finite-size behavior. The domain-wall core energy was computed directly from the Hamiltonian, leading to an estimate of the critical temperature. We reconcile the discrepancies between previous theoretical predictions and numerical results, and further analyze the magnetization scaling to demonstrate how different boundary conditions influence pseudo-critical behavior of finite systems.
We then introduce quenched random fields to investigate how disorder modifies KT-like criticality. Through the analysis of magnetization fluctuations and renormalization group flow behavior, we examine the interaction between domain walls and disorder-induced fragmentation. The results provide a setting where Imry-Ma arguments manifest in systems that exhibit Kosterlitz-Thouless transitions without disorder.
Finally, we experimentally study two-dimensional colloidal crystals with substrate-induced quenched anisotropic disorder. Using microfabricated pinning landscapes and single-particle imaging, we measure structural correlations and defect dynamics across multiple disorder densities. In addition to the characterization of static disorder, we quantify defect lifetimes and hazard rates, revealing spatially varying effective energy barriers introduced by the quenched disorder. These experiments provide a direct dynamical quantification of how quenched disorder reshapes defect-mediated transitions in two-dimensional colloidal crystals.
Biography:
Owen Tower is a PhD candidate in physics at Brown University specializing in statistical mechanics and phase transitions in disordered systems. His research combines large-scale Monte Carlo simulations with analytical techniques to study long-range Ising models and their connections to Kosterlitz-Thouless physics. He has also performed experiments on two-dimensional colloidal crystals to probe disorder-driven melting and defect dynamics. His work explores how topological phase transitions evolve in the presence of quenched disorder.
Note: All PHY Graduate Students are ENCOURAGED to attend.
All interested parties are invited to attend. Open to the public.
SENG 201