Complexity and universality in physical systems: understanding unifying principles behind shared emergent behavior

• Grant number: 24/11114-1
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: February 01, 2025
• End date: January 31, 2030
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Jaron Patrick Kent-Dobias
• Grantee: Jaron Patrick Kent-Dobias
• Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
• Associated scholarship(s): 25/01111-8 - Complexity and Universality in Physical Systems: understanding unifying principles behind shared emergent behavior, BP.JP

Abstract

One of the great marvels of physics is its universality: the same principals applied to one system can apply to other, disparate ones on the other side of the universe. More incredible still is the universality present in emergent phenomena of different constituent parts, e.g., the same critical behavior is found in ferromagnets and liquids. That particular connection is now well understood in terms of the equilibrium renormalization group, but in many cases the question remains: what underlies universal behavior that arises in systems with different component parts? This question is at the forefront of research in two seemingly disparate fields: complex systems and out-of-equilibrium critical phenomena. In the first case, diverse systems including spin glasses, structural glasses, machine learning models, biological networks, and evolutionary dynamics all are thought to share 'glassy' phenomenology: slow dynamics, many metastable states, aging, memory, broken ergodicity. In all, the metaphor of a cost or energy 'landscape' is often used to reason about these shared traits, like under what circumstances they should arise. But can the landscape idea be promoted to more than a metaphor: are there unambiguous structural signatures that connect and make predictions about the behavior in these disparate cases? In the second case, losing equilibrium or tuning to strange nonlinear fixed points removes core assumptions beneath the renormalization group technique, and thus demands new principles and promises to produce new behavior. Can standard assumptions about analyticity, the division into relevant, irrelevant, and marginal variables, and the typical characteristics of fixed points for stable phases and first order transitions be maintained? Specific examples seem to suggest they cannot, but underlying connections between them are lacking. These questions form the basic motivations my research proposals. (AU)