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We explore the effect of single-particle level fluctuations on the Stonerinstability in a QD with a strong spin-orbit coupling in the framework of theuniversal Hamiltonian with the Ising exchange interaction. We reduce theproblem to studying the statistics of extrema of a certain Gaussian process anddemonstrate that, in spite of the randomness of the single-particle levels, thelongitudinal spin susceptibility and all its moments diverge simultaneously atthe point of the Stoner instability which is determined by the standardcriterion involving the mean level spacing only.

Statistics of Spin Fluctuations in Quantum Dots with Ising Exchange