# Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions

## TL;DR

This paper investigates the transition behaviors in a 2D frustrated spin system near a critical point, revealing how chirality phase transitions emerge and exhibit geometric rigidity through variational analysis.

## Contribution

It provides a rigorous variational analysis of the emergence and rigidity of chirality transitions in a discrete spin model as it approaches the continuum limit.

## Key findings

- Chirality phase transitions emerge at the continuum limit.
- The geometric rigidity of these transitions is characterized.
- The analysis is based on $ ext{Gamma}$-convergence of the energy scalings.

## Abstract

We study the discrete-to-continuum variational limit of the $J_{1}$-$J_{3}$ spin model on the square lattice in the vicinity of the helimagnet/ferromagnet transition point as the lattice spacing vanishes. Carrying out the $\Gamma$-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.