Abstract: The distinctive phase transition phenomena of magnetic systems with frozen disorder are studied with renormalization-group theories that are numerically exact for d=3 hierarchical lattices and that have proven to be quite indicative for the physical lattices. A pedagogical introduction will be followed by recent results, including inverted tricritical points , finite-temperature spin-glass order induced by quenched dilution, asymmetric quantum spin-glass phase diagrams. On scale-free small-world spin-glass networks, the calculated local magnetizations and local spin-glass order parameters exhibit, as function of temperature, complex tulip patterns. The conversion of first-order phase transitions to second order and the strong violation of critical phenomena universality, predicted by this approach, has recently been confirmed by numerical simulation.
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