Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions will the temperatures revert, or will we have passed a tipping point beyond which return to the present state is impossible? We address this question with a column model of the Arctic atmosphere based on mathematical representations of the primary physical features, including the Schwarzschild two-stream equations for the long wave radiation, the Clausius-Clapeyron equation for water vapour concentrations, atmosphere absorption characteristics dependent on carbon dioxide and water vapour concentration levels, and nonlinear albedo response to surface temperature. We analyzed solutions of our model under four representative carbon pathways (RCPs) extending into the future. Under the strongest mitigation pathway (which represents far swifter carbon emission reductions than presently seen), the Arctic shows a mild increase in temperature that is reversible. Under the highest carbon pathway (which represents a continuation of the status quo with regard to emissions), the Arctic climate undergoes an irreversible bifurcation to a warm steady state, corresponding to annually ice-free conditions, prior to the end of this century. Under the two intermediate pathways, temperatures increase substantially and the system enters a state of bi-stability where an external perturbation could possible cause an irreversible switch to warm, ice-free state.