The environmental interaction is a fundamental consideration in any controlled quantum system. While an interaction with a dissipative bath can lead to decoherence, it can also provide desirable emergent effects including induced spin-spin correlations. In this Letter, we show that under quite general conditions, a dissipative bosonic bath can induce a long-range ordered phase, without the inclusion of any additional direct spin-spin couplings. Through a quantum-to-classical mapping and classical Monte Carlo simulation, we investigate the $T=0$ quantum phase transition of an Ising chain embedded in a bosonic bath with Ohmic dissipation. We show that the quantum critical point is continuous, Lorentz invariant with a dynamical critical exponent $z=1.07\left(9\right)$, has a correlation length exponent $\nu =0.80\left(5\right)$, and anomalous exponent $\eta =1.02\left(6\right)$, thus the universality class is distinct from the previously studied limiting cases. The implications of our results on experiments in ultracold atomic mixtures and qubit chains in dissipative environments are discussed.

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• Cold gases in optical lattices
• Critical exponents
• Decoherence in quantum gases
• Frustrated magnetism
• Second order phase transitions
• 1-dimensional spin chains
• Ultracold gases
• Monte Carlo methods