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The study of interdependent networks has recently experienced a boost withthe development of experimentally testable materials that physically realizetheir critical behaviors, calling for systematic studies that go beyond thepercolation paradigm. Here we study the critical phase transition ofinterdependent spatial magnetic networks model where dependency couplingsbetween networks are realized by a thermal interaction having a tunable spatialrange. We show how the critical phenomena and the phase diagram of thisrealistic model are highly affected by the range of thermal dissipation and howthe latter changes the transition from continuous to abrupt. Furthermore, weshow that microscopic interventions of localized heating and localized magneticfield yield a macroscopic phase transition and novel phase diagrams. Ourresults provide novel and realistic insights about controlling the macroscopicphases of interdependent materials by means of localized microscopicinterventions.

Microscopic intervention yields abrupt transition in interdependent magnetic networks