Discrepancy in static critical exponents between 3D Heisenberg model with random cubic anisotropy and RSIM

Determine the origin of the discrepancy between the static critical exponents η and ν measured for the three-dimensional Heisenberg model with quenched random cubic anisotropy and the corresponding exponents of the three-dimensional site-diluted Ising model (RSIM), despite renormalization-group predictions that both models share a common universality class.

Background

Field-theoretical renormalization-group analyses predict that the 3D Heisenberg model with random cubic anisotropy belongs to the same universality class as the 3D site-diluted Ising model (RSIM), for both static and dynamic critical behavior.

While the dynamic critical exponent z estimated in this work is compatible with RSIM, previously reported static exponents for the Heisenberg model with cubic anisotropy (η=0.03(1), ν=0.737(8)) differ from RSIM values (η=0.036(1), ν=0.683(2)). Understanding this discrepancy remains unresolved.

References

However, it remains an open problem to understand the difference among the static critical exponents found in the 3D Heisenberg model with cubic anisotropy and those of the RSIM.

— Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy (2410.14275 - Astillero et al., 18 Oct 2024) in Conclusions