  Dissipative processes can drive different magnetic orders in quantum spin
chains. Using a non-perturbative analytic mapping framework, we systematically
show how to structure different magnetic orders in spin systems by controlling
the locality of the attached baths. Our mapping approach reveals analytically
the impact of spin-bath couplings, leading to the suppression of spin
splittings, bath-dressing and mixing of spin-spin interactions, and emergence
of non-local ferromagnetic interactions between spins coupled to the same bath,
which become long-ranged for a global bath. Our general mapping method can be
readily applied to a variety of spin models: We demonstrate (i) a bath-induced
transition from antiferromangnetic (AFM) to ferromagnetic ordering in a
Heisenberg spin chain, (ii) AFM to extended Neel phase ordering within a
transverse-field Ising chain with pairwise couplings to baths, and (iii) a
quantum phase transition in the fully-connected Ising model. Our method is
non-perturbative in the system-bath coupling. It holds for a variety of
non-Markovian baths and it can be readily applied towards studying
bath-engineered phases in frustrated or topological materials.
