Dobrushin Interfaces via Reflection Positivity

TL;DR

This paper employs Reflection Positivity to analyze phase interfaces in 3D systems, demonstrating interface rigidity and simplifying results for models like Ising and Potts, applicable to both discrete and continuous spins.

Contribution

It introduces a Reflection Positivity approach to study interface rigidity in 3D models, unifying analysis across discrete and continuous spin systems.

Findings

Proves interface rigidity in 3D non-linear sigma-models.

Simplifies derivation of known results for Ising and Potts models.

Applicable to large-entropy continuous spin systems.

Abstract

We study the interfaces separating different phases of 3D systems by means of the Reflection Positivity method. We treat discrete non-linear sigma-models, which exhibit power-law decay of correlations at low temperatures, and we prove the rigidity property of the interface. Our method is applicable to the Ising and Potts models, where it simplifies the derivation of some known results. The method also works for large-entropy systems of continuous spins.