Scanning-probe and information-concealing machine learning intermediate hexatic phase and critical scaling of solid-hexatic phase transition in biological tissues

We investigate the two-dimensional melting of biological tissues that are modeled by deformable polymeric particles with multi-body interactions described by the Voronoi model. We identify the existence of the intermediate hexatic phase in this system, and the critical scaling of the associated solid-hexatic phase transition with the critical exponent $ uapprox0.65$ for the divergence of the correlation length. Moreover, we clarify the discontinuous nature of the hexatic-liquid phase transition in this system. These findings are achieved by directly analyzing systems spatial configurations with two generic machine learning approaches developed in this work, dubbed scanning-probe via which the possible existence of intermediate phases can be efficiently detected, and information-concealing via which the critical scaling of the correlation length in the vicinity of generic continuous phase transition can be extracted. Our work provides new physical insights into the fundamental nature of the two-dimensional melting of biological tissues, and establishes a new type of generic toolbox to investigate fundamental properties of phase transitions in various complex systems.