Propagation of an electrostatic surface wave in a thin degenerate Fermi plasma film in the presence of constant external magnetic field is studied here. Dispersion relations for the symmetric and anti-symmetric modes have been derived and studied quantitatively with the exchange–correlation effects. It has been studied that with the increase in the strength of magnetic field, phase velocity of the waves decreases. Also electron exchange–correlation effects significantly modify the behavior of the surface waves such as frequency of surface wave is found to be downshifted by these effects. Moreover it has been studied that the group velocity of the anti-symmetric mode is greater than the symmetric mode for the whole wave numbers; however, these modes merge into a single mode with the increase of the wave number.
