# Double Peak energy distribution for first-order transition points with open boundary condition

I am looking into a first-order phase transition with Monte Carlo simulation, and encountering a puzzling situation with boundary conditions.

More precisely, it is easy to see the characteristic "double peak" of the energy distribution at the transition point when I do the MC simulation on the periodic boundary condition (PBC). This double-peak is usually considered as evidence for phase coexistence at the transition point, which is pretty much the definition of a first-order phase transition.

However, when I simulate the same model but with open boundary condition (OBC), this double peak seems to become considerably harder to observe. At least, I cannot see it with the same system size.

In my understanding, as long as conventional spontaneous symmetry breaking type phase transitions are considered, boundary conditions should not play a crucial role in terms of the nature of the phase transition, especially in the thermodynamic limit. I would guess that if I increase the system size to even larger systems I would eventually be able to observe the double-peak anyway, but this tendency that "OBC is harder to exhibit double-peak energy distributions compared to PBC" seems to be persistent through some models that I tested.

This is a bit surprising, because I can't recall any remarks on this general tendency, especially when it seems pretty robust and strong! For example, in the 10-state Potts model in 2D, L=32 is a size you can reach with a laptop in about an hour to have a reasonably good estimation of the distribution (using methods like Wang-Landau sampling, but that's not important now). With PBC, we can definitely see the double-peak (as suggested in the WL paper https://arxiv.org/abs/cond-mat/0011174), but with L=32 OBC, this double peak seems to almost disappear. It seems that the OBC erases the double-peak for system sizes that are just about the right size that's practical and would have shown a double-peak with the PBC.

Could anyone give me any reference on this phenomena, or any paper that mentions this tendency? I'm thinking there must be some remarks on this phenomenon somewhere because it seems so basic! Thank you for reading this.