Finite size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

TL;DR

This paper investigates the finite size scaling behavior of Villain's fully frustrated model and demonstrates how small plaquette disorder significantly alters the critical scaling laws at zero temperature.

Contribution

It introduces an exact finite volume partition function approach to analyze scaling laws and reveals the dramatic impact of minimal disorder on critical behavior.

Findings

Uncovered an unexpected finite size scaling law in the model.

Small plaquette disorder drastically changes the T=0 critical scaling laws.

Finite volume analysis provides new insights into frustrated spin systems.

Abstract

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T=0 critical point.