Anharmonicity of flux lattices and thermal fluctuations in layered superconductors

We study elasticity of a perpendicular flux lattice in a layered superconductor with Josephson coupling between layers. We find that the energy contains ln(flux displacement) terms, so that elastic constants cannot be strictly defined. Instead we define effective elastic constants by a thermal average. The tilt modulus has terms with ln(T) which for weak fields, i.e. Josephson length smaller than the flux line spacing, lead to displacement square average proportional to T/ln(T). The expansion parameter indicates that the dominant low temperature phase transition is either layer decoupling at high fields or melting at low fields.