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ent lan ne 1 The theory of structural transformation of the vortex lattice in a fourfold symmetric in a–b plane type-II superconductors is con-structed using both the London and the lowest Landau level Ginzburg–Landau model. Thermal fluctuations and quenched disorder influence the location of the square to rhomb structural transition line. The self consistent harmonic approximation for lattice anharmo-systems possessing different lattice symmetry is an old well by the nonlocal London (NLL) theory proposed by Kogan and collaborators [1]. The agreement with theoreti-cal predictions is readily understood conceptually because very reliable. It is assumed that vortices are well separated neutron scattering experiment of Eskildsen et al. [2] on LuNi2B2C suggests that the SPT line sharply bends upwards and even become re-entrant in this region. This is very sur-prising if one assumes that fluctuations of some kind are responsible for such behaviour. Gurevich and Kogan [3] were first to consider the thermal fluctuations. They worked * Corresponding author