The role of dependency range in thermally coupled superconducting networks

Interdependent networks can be highly fragile because dependency links amplify local failures into cascades that trigger global collapse. Much of the theoretical understanding comes from geometric network models, where dependency range is imposed externally and coupling strength is distance independent, and it is unclear how these insights apply to real materials, where interdependence arises from physical transport. Here we study thermally coupled amorphous superconducting networks, in which dependencies emerge from current redistribution and heat-mediated interactions governed by thermal diffusivity. Using an experimentally calibrated model of resistively shunted Josephson junctions, we show the system reproduces the three canonical transition regimes: continuous, nucleation-dominated, and mixed-order. However, because heat-driven dependency simultaneously broadens and weakens with distance, long-range thermal coupling can stabilize the superconducting phase upon heating, in contrast with its destabilizing role in geometric models. Cascades are anisotropic, with one-dimensional front propagation. These results offer an experimentally testable perspective complementing the geometric framework.