An effective field model to high temperature superconductors: Fitting of the energy gap to the experimental results of the Bi2Sr2CaCu2O8

We use an effective field model (transverse Ising model) to describe the de pendence on the temperature of the energy gap of some two-dimensional (2D) superconducting systems. The order parameter of this model is Dot in a dire ct correspondence with that of the Ising model. Then, we use the exact rela tions for the spontaneous magnetization of the Ising model in some 2D latti ces as a means to fit the experimental results of Bi2Sr2CaCu2O8 films obtai ned through reflectivity measurements by Brunel ct al. [Phys. Rev. Lett. 66 , 1346 (1991)] and the argon-annealed Bi2Sr2CaCu2O8 samples investigated by Staufer ct al. [Phys. Rev. Lett. 68, 1069 (1992)] through Raman scattering . The zero temperature energy gap E-g(0) relations were evaluated in variou s 2D lattices and also in the (3D) simple cubic lattice for comparison. In the square lattice case, we obtained E-g(0) = 3.52kT(c), coincidentally the same number as the BCS result, and in the triangular lattice case, we get E-g(0) = 3.30kT(c), in agreement with the experimental findings of Brunel c t al.(13).