##
Mean Field Theory for Arrays of Josephson-Coupled Wires

#### J. Kent Harbaugh and D. Stroud, Department of Physics,
The Ohio State University, Columbus, Ohio 43210-1106

We describe a mean-field theory for phase transitions in a
Josephson junction array consisting of two sets of parallel wire networks,
arranged at right angles and coupled together by Josephson interactions.
In contrast to earlier treatments, we include the variation of the
superconducting phase along the individual wires; such variation is always
present if the wires have finite thickness and are sufficiently long. The
mean field result is obtained by treating the individual wires exactly and
the coupling between them within the mean field approximation. For a
perpendicular applied magnetic field of strength $p/q$ flux quanta per
plaquette (where $p$ and $q$ are mutually prime
integers), we find that the mean-field transition temperature $T_c(f)
\approx T_c(0)q^{-b}$ with $b = 1/4$. By contrast, a mean-field theory
which neglects phase variation along the array predicts $b = 1/2$, and
gives a $T_c$ which diverges in the thermodynamic limit. The model with
phase variations agrees somewhat better with experiment on large arrays
than does the approximation which neglects phase variations.
PACS Nos.: 74.50.+r, 74.25.Bt, 74.40.+k, 74.80.-g