Determination of the nearest-neighbor interaction in VO2 via fractal dimension analysis

The Ising model is one of the simplest and most well-established concepts to simulate phase transformations in complex materials. However, its most central constant, the interaction strength J between two nearest neighbors, is hard to obtain. Here we show how this basic constant can be determined with a fractal dimension analysis of measured domain structures. We apply this approach to vanadium dioxide, a strongly correlated material with a first-order insulator-to-metal phase transition with enigmatic properties. We obtain a nearest-neighbor interaction of 13.8 meV, a value close to the thermal energy at room temperature. Consequently, even far below the transition temperature, there are spontaneous local phase flips from the insulating into the metallic phase. These fluctuations explain several measured anomalies in VO2, in particular the low thermal carrier activation energy and the finite conductivity of the insulating phase. As a method, our fractal dimension analysis links the Ising model to macroscopic material constants for almost any first-order phase transition.