Stripe order, impurities, and symmetry breaking in a diluted frustrated magnet

TL;DR

This study explores how weak spatial anisotropies can restore stripe order in a diluted frustrated Ising model, revealing a logarithmic relationship between transition temperature and anisotropy strength, with critical behavior akin to the disordered 2D Ising universality class.

Contribution

It demonstrates that even minimal spatial anisotropies can re-establish stripe order in a diluted frustrated magnet, providing a quantitative relationship and analyzing the critical behavior.

Findings

Weak anisotropies restore stripe order despite impurities.

Transition temperature scales as 1/|ln(ΔJ)| for small anisotropies.

Critical behavior belongs to the disordered 2D Ising universality class.

Abstract

We investigate the behavior of the frustrated $J_1$-$J_2$ Ising model on a square lattice under the influence of random dilution and spatial anisotropies. Spinless impurities generate a random-field type disorder for the spin-density wave (stripe) order parameter. These random fields destroy the long-range stripe order in the case of spatially isotropic interactions. Combining symmetry arguments, percolation theory and large-scale Monte Carlo simulations, we demonstrate that arbitrarily weak spatial interaction anisotropies restore the stripe phase. More specifically, the transition temperature $T_c$ into the stripe phase depends on the interaction anisotropy $\Delta J$ via $T_c \sim 1/|\ln (\Delta J)|$ for small $\Delta J$. This logarithmic dependence implies that very weak anisotropies are sufficient to restore the transition temperature to values comparable to that of the undiluted system. We analyze the critical behavior of the emerging transition and find it to belong to the disordered two-dimensional Ising universality class, which features the clean Ising critical exponents and universal logarithmic corrections. We also discuss the generality of our results and their consequences for experiments.