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In a scenario of spontaneous symmetry breaking in finite time, topologicaldefects are generated at a density that scale with the driving time accordingto the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZMhave recently been unveiled: The number distribution of topological defects hasbeen shown to follow a binomial distribution, in which all cumulants inheritthe universal power-law scaling with the quench rate, with cumulant rationsbeing constant. In this work, we analyze the role of boundary conditions in thestatistics of topological defects. In particular, we consider a lattice systemwith nearest-neighbor interactions subject to soft anti-periodic, open, andperiodic boundary conditions implemented by an energy penalty term. We showthat for fast and moderate quenches, the cumulants of the kink numberdistribution present a universal scaling with the quench rate that isindependent of the boundary conditions except by an additive term, that becomesprominent in the limit of slow quenches, leading to the breaking of power-lawbehavior. We test our theoretical predictions with a one-dimensional scalartheory on a lattice.

Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition