---
title: "Vortex unbinding: a two-dimensional fluid could change without ordinary order"
description: "How can vortex pairs drive a transition in two dimensions?"
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  zh-CN: "https://sandboxphysics.com/zh/stories/condensed-matter/kt-vortex-unbinding/"
last_modified: "2026-10-23"
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[Magnetism, disorder and topological response](https://sandboxphysics.com/stories/condensed-matter/#magnetism)

Materials · Measurements · Explanation

# Vortex unbinding: a two-dimensional fluid could change without ordinary order

How can vortex pairs drive a transition in two dimensions?

Sandbox Physics · 2026-10-23

Nobel contribution: 2016-1

1. Consider a two-dimensional phase field
2. Create vortices and antivortices
3. Compare binding with entropy
4. Look for the stiffness change

The thermal vortex transition differs from a band Chern transition and from a three-dimensional vortex lattice.

## Two dimensions altered the ordering question

Kosterlitz and Thouless developed their vortex account in work published in 1972 and 1973. A two-dimensional system with a continuous phase can lack ordinary long-range order yet retain a low-temperature state with slowly decaying correlations.

Topology enters through vortices: phase winds around their centers. The 2016 award recognized this transition theory alongside other discoveries of topological matter.

Sources: [1] [2]

## Binding competes with the number of possible positions

At low temperature, opposite vortices tend to form bound pairs. Raising temperature makes the entropy gained by separating them increasingly important. Unbound vortices disrupt phase coherence over long distances, producing a transition with unusual scaling.

Sources: [1]

## Stiffness supplies a physical test

The response to a phase twist measures the system’s stiffness. Its characteristic behavior near the transition links the abstract vortex picture to experiments on suitable thin films and two-dimensional fluids. Finite size and inhomogeneity can round the observed change.

Sources: [1]

## Existing models supply comparisons, not a duplicate

The occupation model explains Bose statistics, while the critical-field model shows magnetic vortices in a different setting. Neither implements a thermal two-dimensional vortex-unbinding simulation. That distinction preserves the content of the theory instead of merging every vortex picture into one.

Sources: [1] [2] [3]

Continue with the physics

## Try the related models

### [Quantum gas occupation](https://sandboxphysics.com/labs/quantum-gas-occupation/)

Lower temperature and compare Bose and Fermi occupations.

Equilibrium occupations alone do not reconstruct a time-of-flight absorption image or establish superfluidity.

### [Superconducting critical fields](https://sandboxphysics.com/labs/superconductor-critical-fields/)

Compare flux exclusion, vortex entry and destruction of superconductivity.

The isotropic Ginzburg–Landau model applies near the transition and is not a quantitative cuprate phase diagram.

## Sources and reading notes

1. [2016 Nobel scientific background: topology and phases of matter](https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2016.pdf)

   Vortex unbinding, integer-spin chains and quantized Hall topology are different theoretical results.

2. [Thouless: account of vortex transitions and Hall topology](https://www.nobelprize.org/prizes/physics/2016/thouless/biographical/)

   Connects the vortex work with Kosterlitz and the later four-author Hall-conductance paper.

3. [Nobel Prize in Physics 2016: official award](https://www.nobelprize.org/prizes/physics/2016/summary/)

   Official attribution and award year. The observation or theoretical paper may be much earlier.

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