Role of four-spin exchange in a magnetic mechanism of superconductivity in cuprates

Amendments to the exchange interaction can alter the superconducting transition temperature, so on the basis of numerical self-consistent solution of two equations in the framework of the $t$-$J$ model, we investigate the influence of the four spin exchange on the concentration dependence of the transition temperature to the superconducting phase with $d_{x^2-y^2}$ – the type of symmetry of the order.