Fig. 2: Ensuring that the zero-temperature limit has been reached by comparing PBCs and APBCs over Euclidean time.
From: The quantum transition of the two-dimensional Ising spin glass
a, Correlation length ξ(3) (‘One-time observables’ in Methods) versus k, as computed for our largest systems with L = 24 and Lτ = 2,048 and with both PBCs and APBCs for the same set of 1,280 samples. The statistical agreement for PBCs and APBCs indicates that the T → 0 limit has been effectively reached for this quantity. b, As a for the Binder cumulant (‘One-time observables’ in Methods). The dashed line represents the critical point, kc ≈ 0.29. c, The even correlation functions Q2(τ) (‘Two-times observables’ in Methods), as computed for a single sample of L = 20 at k = 0.29, rather quickly reach their large-τ plateau. The functions depend on both Lτ and the boundary conditions. The PBC plateau decreases upon increasing Lτ, whereas the APBC plateau notably increases. The reason behind the stronger sensitivity of Lτ for APBCs is understood (‘The limit of zero temperature’ in Methods). Points in a, b, and c are statistical averages, and errors are one standard deviation. Our data set is fully described in Extended Data Table 1.
