Table 1 Lattice lengths at the local minima \(\ell _{j}^{(m)}\) and local maxima \(\ell _{j}^{(M)}\) of the density criterion \(N\widetilde{\sigma }\) for the \(J_{x}\) and homogeneous lattice.
z | \(J_{x}\) | Homogeneous | z | \(J_{x}\) | Homogeneous |
|---|---|---|---|---|---|
\(\ell _{1}^{(m)}\) | 0.48781 | 1.1968 | \(\ell _{1}^{(M)}\) | 0.6579 | 1.6099 |
\(\ell _{2}^{(m)}\) | 0.78735 | 1.9211 | \(\ell _{2}^{(M)}\) | 0.9256 | 2.2285 |
\(\ell _{3}^{(m)}\) | 1.11393 | 2.8088 | \(\ell _{3}^{(M)}\) | 1.2227 | 2.9441 |
\(\ell _{4}^{(m)}\) | 1.32647 | 3.3290 | \(\ell _{4}^{(M)}\) | 1.4293 | 3.5156 |
\(\ell _{5}^{(m)}\) | 1.52812 | 4.1988 | \(\ell _{5}^{(M)}\) | \(\pi /2\) | 4.3984 |
\(\ell _{6}^{(m)}\) | Â | 5.1835 | \(\ell _{6}^{(M)}\) | Â | 4.8832 |
\(\ell _{7}^{(m)}\) | Â | 5.6182 | \(\ell _{7}^{(M)}\) | Â | 5.4811 |
| Â | Â | Â | \(\ell _{8}^{(M)}\) | Â | 6.1544 |
