Stability of the Coulomb phase in spin ice at finite temperature

The temperature dependence of the concentration of magnetic monopoles in spin ice has been analyzed. It has been shown that magnetic Coulomb interaction between monopoles can lead to a temperature-induced stepwise increase in their concentration by several orders of magnitude. This first-order phase transition is also accompanied by a decrease in the relaxation time by several orders of magnitude and can be considered as the melting of the Coulomb phase of spin ice. The phase diagram, as well as the critical point, has been determined.