2,351 research outputs found
Infinite Body Centered Cubic Network of Identical Resistors
We express the equivalent resistance between the origin and any other lattice
site in an infinite Body Centered Cubic (BCC) network consisting of identical
resistors each of resistance R rationally in terms of known values and . The
equivalent resistance is then calculated. Finally, for large separation between
the origin and the lattice site two asymptotic formulas for the resistance are
presented and some numerical results with analysis are given.Comment: 13 pages, 2 figure
N=4 SYM on S^3 with Near Critical Chemical Potentials
We study the N = 4 theory at weak coupling, on a three sphere in the grand
canonical ensemble with R symmetry chemical potentials. We focus attention on
near critical values for the chemical potentials, above which the classical
theory has no ground state. By computing a one loop effective potential for the
light degrees of freedom in this regime, we show the existence of flat
directions of complex dimension N, 2N and 3N for one, two and three critical
chemical potentials respectively; these correspond to one half, one quarter and
one-eighth BPS states becoming light respectively at the critical values. At
small finite temperature we show that the chemical potentials can be continued
beyond their classical limiting values to yield a deconfined metastable phase
with lifetime diverging in the large N limit. Our low temperaure analysis
complements the high temperature metastability found by Yamada and Yaffe. The
resulting phase diagram at weak coupling bears a striking resemblance to the
strong coupling phase diagram for charged AdS black holes. Our analysis also
reveals subtle qualitative differences between the two regimes.Comment: 34 pages, 4 figure
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