Fig. 2: Phase transition from order parameter.
From: Non-equilibrium critical scaling and universality in a quantum simulator
We report scaled maximum net correlator \({{{{\mathcal{M}}}}}^{2}={\max }_{t}[\langle {C}_{x}^{2}\rangle /{N}^{2}]\) as a function of \({B}^{z}/{{{\mathcal{J}}}}\) for system sizes N = 10, 15, 20. The solid lines are obtained by fitting the experimental data to the finite size corrected order parameter (Eq. (28) of SI), which has the critical point as a fit parameter. The extracted values are 0.83 (19), 0.88 (6), 1.01 (9), respectively for N = 10, 15, 20; the difference from the predicted critical point \({B}^{z}/{{{\mathcal{J}}}}=1\) is due to finite-size effects and experimental imperfections. For simplicity, we use the predicted critical value for studies in Figs. 3, 4. The dashed line represents the mean-field solution with an inflection point at \({B}^{z}/{{{\mathcal{J}}}}=1\). For the comparison of the experimental data against decoherence-free numerical simulation, see Supplementary Fig. 2. The error bars are statistical fluctuations around the mean value.
