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The mechanical stability of a Aux-line lattice (FLL) having parameters appropriate for the high-T, superconductors is determined using the self-consistent phonon theory of lattice dynamics. Nearly parallel Aux lines (FL's) are assumed and FL pinning is neglected. The FLL becomes unstable when a phonon frequency goes to zero. At instability the rms vibrational amplitude diverges and the FL's can no longer be localized. In Bi2Sr2CaCuO&08, the instability line as a function of temperature anddoi:10.1103/physrevb.45.2409 pmid:10001764 fatcat:vmbymc4zavg6rowm4c2apwb3bq