Weak first-order phase transition out of the classical kagome spin liquid

The low-temperature fate of the spin-liquid regime in the classical kagome Heisenberg antiferromagnet has been debated for over three decades. Using an expansion in the number of spin components, we show that, contrary to earlier Monte Carlo simulations, the spin liquid terminates at a weak first-order phase transition into the $\sqrt{3}\times\sqrt{3}$ phase which ordered moment saturates at zero temperature. Adding second-neighbor interactions, this transition belongs to a line of first-order phase transitions that ends at a critical point. For comparison, the pyrochlore antiferromagnet remains disordered at all temperatures.