Abstract:
We construct a new and efficient cluster algorithm for
updating strongly coupled U(N) lattice gauge theories with
staggered fermions in the chiral limit. The algorithm uses
the constrained monomer-dimer representation of the theory
and should also be of interest to researchers working on
other models with similar constraints. Using the new
algorithm we address questions related to the chiral limit
of strongly coupled U(N) gauge theories beyond the mean
field approximation. We show that the infinite volume chiral
condensate is non-zero in three and four dimensions.
However, on a square lattice of size $L$ we find $\sum_x \sim L^{2-\eta}$ for large
$L$ where $\eta = 0.420(3)/N + 0.078(4)/N^2$. These results
differ from an earlier conclusion obtained using a different
algorithm. Here we argue that the earlier calculations were
misleading due to uncontrolled autocorrelation times
encountered by the previous algorithm.
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