Ordering of Diffusing Spins in Brownian Spin Models

Explore the phase transitions of Brownian spin models in two dimensions during this 45-minute talk from the Thematic Programme on "Large Deviations, Extremes and Anomalous Transport in Non-equilibrium Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the competition between spin fluctuation dynamics and particle density fluctuation dynamics in Brownian Potts and clock models. Discover how diffusion affects phase transitions, leading to continuous transitions in q-state Potts models for q>4, contrasting with discontinuous transitions in equilibrium lattice systems. Examine the double BKT transitions in p-state clock models for q>4, including paramagnetic, quasi-long range ordered, and ordered phases. Gain insights from numerical simulation results and analytical arguments on the universal nature of these phase transitions. Consider potential extensions of this research to systems with self-propelled active particles, building upon the work with passive Brownian particles.