Before revision:  They define analogues of magnetic field h and the inverse temperature (\beta) in Ising model\beta*\beta* \beta*  . Sparks terminate via a phase transition known as "hpolarity reversal" and the leak emerges when hfails to change its sign.
After revision:  They define analogues of magnetic field h and the inverse temperature (\beta) in Ising model\beta*\beta* and a disordered leak occurs when \beta<\beta* . Sparks terminate via a phase transition known as "hpolarity reversal" and the leak emerges when hfails to change its sign.