We investigate the behavior of the frustrated J1-J2 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 Tc into the stripe phase depends on the interaction anisotropy ΔJ via Tc∼1/|ln(ΔJ)| for small ΔJ. 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.




The work in Missouri has been supported in part by the National Science Foundation under Grants No. DMR-1828489 and No. OAC-1919789.

International Standard Serial Number (ISSN)

2469-9969; 2469-9950

Document Type

Article - Journal

Document Version

Final Version

File Type





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Publication Date

04 Jan 2022

Included in

Physics Commons