Extended Data Table 1 Parameters of fixed sector simulations in the pure gauge theory
From: Calculation of the axion mass based on high-temperature lattice quantum chromodynamics
- The first column gives the gauge coupling, the second is the temperature in units of the transition temperature Tc, the third is the lattice extent, the fourth is the collected statistics in millions of updates, the fifth shows the Q sectors used and the last column gives the acceptance rates in the Q > 0 sectors. The first block of parameters shows an Ns scan for which we fixed the gauge coupling and the temperature and varied the spatial extent of the lattice. The second block contains an Nt scan corresponding to a continuum extrapolation. Here the physical volume was fixed. In the Q scan we studied all topological charge sectors from Q = 0 to Q = 8. The last block corresponds to a temperature scan for which we fixed temporal lattice extent and changed the temperature from 1.2Tc up to 7Tc. In the trivial sector we always achieved an acceptance of 100%, which simply reflects the fact that at high temperatures the probability of exploring non-trivial topologies is very small. In the Q = 1 sector, the acceptance was about 70% on the coarsest lattice. For this we had to switch off the overrelaxation step, which makes large moves in the configuration space, and would have almost always resulted in a topology change. On finer lattices, the acceptance was around 90% or better even in the presence of overrelaxation. In the Q > 1 sectors, the acceptance gradually decreased as charge was increased; a simple explanation of this is that the disappearance probability of multiple instantons is approximately the sum of the individual disappearance probabilities. The worst acceptance was around 65% on an 8 × 643 lattice in sector Q = 8.
