Conductance peak motion due to a magnetic field in weakly coupled chaotic quantum dots

We study the influence of moderate exchange interactions of electrons on the behavior of the peaks in the conductance of single electron transistors. We numerically reproduce recently observed features of both the peak positions and the peak heights magnetic field dependence. These features unambiguously identify the total spin $S$ of each ground state. We evaluate the probability of each $S$ (combination of spontaneous and induced magnetization) as a function of the exchange strength, $J$, and external magnetic field, $B$. The expressions involve only $J$ and $g$-factor as adjustable parameters. Moreover, in a surprisingly broad parameter range these probabilities are determined by certain linear combinations of $J$ and $B$.