Random loop models and quantum spin systems

Project funded by Swedish Research Council (Project grant), grant 2015-05195_VR. Participating organisations named by the source: University of Gothenburg. Funded amount: SEK 3,400,000, as stated by the source. Runs 2016-01-01 to 2019-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Sannolikhetsteori och statistik, Probability Theory and Statistics. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-05); national funding data, not CORDIS. Abstract given by the source: Among the most fascinating phenomena in nature are phase transitions, such as when liquid water changes to steam or when metals above a certain temperature cease to be magnetic. The goal of this project is to advance the mathematical understanding of phase transitions by applying innovative probabilistic approaches to quantum spinsystems. Such systems play a central role in the theory of phase transitions and are therefore highly important to mathematicians and physicists alike, both from a theoretical and practical point of view. Despite significant work in the area, including convincing non-rigorous arguments from the field of physics, key models for phase transitions such as the Heisenberg ferromagnet have yet to be rigorously understood. This project will contribute to our understanding of the Heisenberg model and related relevant models, by providing new results, insights, and perspectives on these complex systems, cast in the language of probability theory. We will apply, and also develop, methods known as loop-representations of quantum spin-systems. These allow to formulate the key questions about the model using random, geometrical objects. Similar methods have been a huge success in related models, such as the classical Ising model. Specifically we aim to identify new loop-representations and their applications; use modern probabilistic and analytic techniques in their study; and to determine the behaviour of quantum spin-systems in novel geometries. In addition to making important progress on these mathematical models, in the long term I hope that this project will make a lasting contribution by inspiring a broad audience of researchers working on these fascinating questions.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Random loop models and quantum spin systems" is funded by the Swedish Research Council with a grant of SEK 3,400,000, running from 2016 to 2019. It aims to enhance the mathematical understanding of phase transitions using probabilistic approaches in quantum spin systems. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.