We study QCD with nonzero chemical potential on 44 lattices by averaging over the canonical partition functions, or sectors with fixed quark number. We derive a condensed matrix of size 2×3×L3 whose eigenvalues can be used to find the canonical partition functions. We also experiment with a weight for configuration generation which respects the Z(3) symmetry which forces the canonical partition function to be zero for quark numbers that are not multiples of three.
We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.
Every function of n inputs can be efficiently computed by a complete network of n processors in such a way that: If no faults occur, no set of size t n /2 of players gets any additional information (other than the function value), Even if Byzantine faults are allowed, no set of size t n /3 can either disrupt the computation or get additional information. Furthermore, the above bounds on t are tight!