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

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