Performance of simulated annealing in p-spin glasses

We perform careful numerical simulations of slow Monte-Carlo annealings in the dense 3-body spin glass model and compare with the predictions from different theories: thresholds states, isocomplexity, following state. We conclude that while isocomplexity and following state both provide excellent agreement the numerical data, the influence of threshold states -- that is still the most commonly considered theory -- can be excluded from our data.