Phase Transitions in Disordered LC Systems: A Classical Analog of Quantum Transitions

This paper investigates percolation transitions in a disordered L-C system composed of inductors and capacitors (non-dissipative reactive elements). These transitions occur between different percolating states, resulting in distinct, constant values of the effective conductivity. We employ an exact approach based on the rotational symmetry of two-dimensional DC equations. A new type of phase transition is identified for these non-dissipative systems by analogy to a topological transition. The characteristics of these transitions, which are analogs of topological invariants, are calculated. We propose that these transitions may be considered a classical analog to quantum transitions, such as the quantum Hall effect.