Extended Data Fig. 4: Cooling rate dependence of thermodynamic quantities.
From: Ideal non-crystals as a distinct form of ordered states without symmetry breaking
The temperature dependence of potential energy per particle E (a), pressure p (b), steric order parameter Θ (c), and hexatic bond-orientational order parameter Ψ6 (d) for cooling rates covering three orders of magnitude. For particle \(j,{\Psi }_{6}^{j}=| {\Sigma }_{k}{e}_{jk}^{6i\theta }/{n}_{j}|\), where nj is the number of nearest neighbors of particle j, and θjk is the angle of the bond rjk = rj − rk with respect to the x-axis. Insets provide enlarged views of the low-temperature regime. The dashed line indicates the lowest temperature, T = 2 × 10−4, down to which results from different cooling rates converge, ensuring equilibration by swap Monte Carlo simulations. Importantly, in panel d, Ψ6 shows a peak around T = 1.4 × 10−3, below which Ψ6 significantly decreases with temperature, indicating that the hexatic crystalline order is thermodynamically unfavourable in our system.
