Bulk-Boundary Correspondence In Soft Matter : From Fractals to Order Parameter*

In recent years, bulk-boundary correspondence (BBC) has been one of the hot topics both in solid state physics (topological materials) and high energy theory (holography and gauge/gravity duality).
Our work is the first ever exposition of BBC yet in another domain; soft condensed matter. We for the first time hypothesize and confirm that BBC also holds in soft matter.
Instead of studying the bulk nature of LC+aerosil gels –like the classical works of x-ray scattering and heat capacity measurements- we chose to study the surface of these gels usinf atomic-force microscopy (AFM) techniques where we managed to correlate the surface related parameters with the ones of the bulk. The essence of our study is based on the created randomness which can be systematically controlled. This is the aerosil amount in the gels. Here we study the surface effects as functions of the disorder strengths created in the 8CB+aerosil gels samples. The correspondence between the bulk (order parameter; beta) and the surface parameters (fractal dimensions) are systematically studied as functions of disorder strength (aerosil amount in the samples).