Fig. 4

Orientational and positional order of the vortex and Bragg glass phases of Bi\({}_{2}\)Sr\({}_{2}\)CaCu\({}_{2}\)O\({}_{8+\delta }\) vortex matter at the surface of electron-irradiated samples A and B. Data obtained from magnetic decoration experiments. a Orientational correlation function \({G}_{6}\) for various normalized fields \(B/{B}_{{\rm{ord-dis}}}\), with \({B}_{{\rm{ord-dis}}}\) the order–disorder transition field. Arrows indicate the size of crystallites. b Displacement correlator \({W}^{* }/{a}_{0}^{2}\) calculated using the lanes algorithm avoiding the effect of topological defects. Data shown following the same color-code as in a. Insert: detail of the fit for data obtained at \(B/{B}_{{\rm{ord-dis}}}=1.62\). Dashed lines correspond to fits with an algebraic decay whereas full lines are exponential fits. c Exponents from the algebraic fittings of \({G}_{6}(r)\) (left axis, squares) and of \({W}^{* }(r)/{a}_{0}^{2}\) (right axis, triangles) for the Bragg and vortex glass phases of pristine P and electron-irradiated A and B samples. The dashed red line indicates the characteristic value of \(\nu =0.44\) expected for the random manifold regime. d Field-evolution of the displacement correlator at a fixed lattice spacing, \({W}^{* }(r/{a}_{0}=10)/{a}_{0}^{2}\). In all panels error bars correspond to the standard error of the mean