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2008 Kac Lecture Series Reception/ Refreshments Served 9:30am In a classical plasma (or an electrolyte solution) the chargecharge structure factor obeys *formula* , where *formula* and *formula* are the second and fourthmoment chargecharge correlation lengths depending on T and the overall ionic density *formula* . The vanishing of the leading term, the first StillingerLovett (SL) sum rule [1], simply reflects bulk electroneutrality. The second SL rule [1], or secondmoment condition, dictates that *formula* where the Debye screening length *formula* varies as *formula*, *formula* being the elementary charge. Recent grandcanonical Monte Carlo simulations [2] of a fully size and chargesymmetric 1:1 (finely discretized) hardsphere plasma or restricted primitive model [3], impose electroneutrality and so satisfy SL1 automatically. However, careful finitesize scaling analyses of extensive histogramreweighted data indicates that the secondmoment condition is violated at criticality by approximately 10%, *formula*. It is also found that *formula* diverges to *formula* in a manner that seems to mirror the densitydensity fluctuation. These findings contradict Generalized DebyeHückel theory [4] and also the exactly soluble chargesymmetric spherical models [5] both of which support SL2 at criticality and the finiteness of the fourthmoment. Nevertheless, the observed behavior is strikingly similar to that of the chargeasymmetric spherical models [5] where SL2 fails at criticality while diverges as *formula*. [1] F.H. Stillinger and R. Lovett, J. Chem. Phys. 48, 3858 (1968). [2] Work with S.K. Das and Y.C. Kim (to be published). [3] See, e.g., Y.C. Kim and M.E. Fisher, Phys. Rev. Lett. 92, 185703 (2004). [4] B.P. Lee and M.E. Fisher, Europhys. Lett. 39, 611 (1997). [5] J.N Aqua and M.E. Fisher, Phys. Rev. Lett. 92, 135702 (2004). For Additional Information Please Visit Our Website: http://cnls.lanl.gov/External/Kac.php Host: Robert Ecke 