2026 IoP Special Lecture Series on Anderson-Yuval-Kosterlitz renormalization-group theory

2 Feb 2026, 13:30 → 23 Feb 2026, 16:00 Asia/Taipei

P101 Classroom (IoP Building, Academia Sinica)

Chen-Hsuan Hsu (Institute of Physics, Academia Sinica, Taiwan)

Welcome to the 2026 Institute of Physics (IoP) Special Lecture Series on Anderson-Yuval-Kosterlitz renormalization-group theory. This special lecture series will be delivered by Prof. Xinsheng Sean Ling (凌新生教授) from Brown University. 

Introduction to the renormalization-group theory of Anderson-Yuval-Kosterlitz for 1D Ising model with 1/r^2 interactions.  

Abstract: The 1D Ising model with 1/r^2 interactions is believed to have a finite-temperature phase transition as argued by Dyson and Thouless using scaling arguments. There is still no exact solution to this model. The renormalization-group (RG) theory developed by Anderson and Yuval and later by Kosterlitz provides a clear physical picture of a phase transition driven by the unbinding topological defects. The same ideas were applied to 2D XY model by Kosterlitz and Thouless and led to the discovery of the Kosterlitz-Thouless transition (for which they were awarded the 2016 Nobel Prize in Physics).  In this series of five lectures, Professor Sean Ling will discuss the pedagogy of the Anderson-Yuval-Kosterlitz (AYK) RG theory and will discuss new research opportunities in this area.

*Students are expected to have taken one year (at least one semester) of statistical mechanics course (Kerson Huang's textbook or similar) and are in command of the concepts of partition functions and thermodynamics. 

**No registration is required. 

In addition to the lectures, Professor Sean Ling will have the opportunity to engage in further discussions until mid April. For those interested in scheduling private discussions, please contact Dr. Chen-Hsuan Hsu at chenhsuan[at]as.edu.tw or Ms. Yu-Hsin Chen at yhmchen[at]as.edu.tw. 

Monday 2 February

14:00 → 15:30 Lecture 1

Brief review of phase transitions and critical phenomena: Ising models, 1D Ising model with 1/r^2 interactions Thouless argument

Convener: Prof. Xinsheng Sean Ling (Brown University)

Wednesday 4 February

14:00 → 15:30 Lecture 2

Scaling and invariance: Kadanoff decimation, RG equations, fixed points, AYK derivation of RG equations.

Convener: Prof. Xinsheng Sean Ling (Brown University)

Monday 9 February

14:00 → 15:30 Lecture 3

Full derivation of AYK RG equations

Convener: Prof. Xinsheng Sean Ling (Brown University)

Wednesday 11 February

14:00 → 15:30 Lecture 4

Solutions of the AYK RG equations and how to use these solutions.

Convener: Prof. Xinsheng Sean Ling (Brown University)

Monday 23 February

14:00 → 15:30 Lecture 5

Determination of the critical temperature: Finite-size scaling and Monte Carlo simulations, and unresolved issues and opportunities

Convener: Prof. Xinsheng Sean Ling (Brown University)