Limit Shapes and Their Phase Transitions - Classical and Quantum

Explore limit shapes and their phase transitions in both classical and quantum systems through this 49-minute conference talk delivered at the International Centre for Theoretical Sciences. Delve into the mathematical frameworks that describe how microscopic interactions give rise to macroscopic geometric patterns and understand the critical phenomena that occur at the boundaries between different phases. Examine the fundamental differences and surprising similarities between classical statistical mechanics and quantum many-body systems when analyzing limit shape formation. Learn about the theoretical tools and computational methods used to predict and characterize these emergent geometric structures, including their stability, fluctuations, and response to external perturbations. Discover how limit shapes manifest in various physical contexts, from crystal growth and particle systems to quantum spin chains and cold atomic gases. Gain insights into the universal aspects of phase transitions that govern the evolution of these shapes and their connection to broader concepts in statistical physics and condensed matter theory.