Determine whether long-range order exists at the partition-function minimum

Determine whether long-range order exists at the point phi=pi/8 and K0.16017, where the generalized BaxterWu model with asymmetric complex-conjugate couplings exhibits its most severe sign problem, by establishing the thermodynamic-limit behavior beyond the finite-size range accessible to the simulations.

Background

The authors observe a local peak in the squared order parameter near phi=pi/8, corresponding to a minimum of the partition function and the strongest sign problem. Although the peak decreases with increasing system size, the severe sign cancellations prevent simulations on sufficiently large lattices for a definitive finite-size extrapolation. Consequently, the existence or absence of long-range order at the anomalous point cannot be conclusively settled by the reported data.

References

However, since the sign problem is most severe at this point, we are unable to simulate larger system sizes to perform a finite-size extrapolation and thus cannot rule out long-range order at this point.

— Periodicity-driven revision of the phase diagram of the generalized Baxter-Wu model with asymmetric complex couplings  (2608.14030 - Wang et al., 14 Aug 2026) in Section 3.1, subsection “Monte Carlo verification of the complete self-dual phase diagram”