Efficient multicanonical sampling at low temperature

Construct a multicanonical sampling scheme with a second reaction coordinate that overcomes the barriers orthogonal to $E_\Delta$ and restores efficient tunneling between the coexisting phases of the honeycomb-lattice Blume–Capel ferromagnet near $T=0.20$.

Background

The paper uses a multicanonical ensemble in the crystal-field energy variable EΔE_\Delta to measure the interface tension and coexistence line in the first-order regime. This approach is effective over much of the studied temperature range but becomes inefficient at the low-temperature end.

Near T=0.20T=0.20, some simulations remain trapped for a substantial fraction of their runtime even when using identical weights. The authors attribute this to barriers associated with changes in droplet shape at fixed density, which are orthogonal to EΔE_\Delta and therefore are not removed by the one-coordinate multicanonical ensemble. They explicitly identify a second reaction coordinate as necessary.

References

At the low-temperature end, a multicanonical ensemble in $E_\Delta$ alone ceases to be efficient near $T=0.20$, where tunneling between the phases is limited by barriers orthogonal to $E_\Delta$; a second reaction coordinate would be needed there.

— High-resolution mapping of the phase boundary of the honeycomb-lattice Blume--Capel ferromagnet  (2610.11068 - Filho et al., 8 Oct 2026) in Section “Summary and outlook”