On the growing length scale in a replica-coupled glassforming liquid

Computer simulations are used to study a three-dimensional polydisperse model glassformer in a replica-coupling setup where an attractive field $\propto -\epsilon Q$ of strength $\epsilon$ can adjust the similarity of the system to a fixed reference configuration with the overlap parameter $Q$. The polydispersity in the model enables the efficient use of swap Monte Carlo in combination with molecular-dynamics simulation from which we obtain fully equilibrated liquid configurations at very low temperature, i.e., far below the critical temperature of mode-coupling theory, $T_{\mathrm{M}\mathrm{C}\mathrm{T}}$. When the $\epsilon$-field is switched on, the fast dynamics with swaps allow relaxation to the stationary state at temperatures below $T_{\mathrm{M}\mathrm{C}\mathrm{T}}$. In the stationary state, the overlap $Q$ has a finite value that increases with increasing $\epsilon$. For a given temperature $T$, fluctuations of the overlap around the average value become maximal at a critical field strength ${\epsilon }^{\star }(T)$. With decreasing $T$ along this ${\epsilon }^{\star }(T)$-line, overlap fluctuations increase and a transition from a unimodal overlap distribution to a bimodal shape occurs. We give evidence that these bimodal distributions are not due to first-order phase transitions. However, they reflect finite-size effects due to a rapidly growing length scale with decreasing temperature. We discuss the significance of this length scale for the understanding of the glass transition.