Abstract : The subject of the first part is the behavior at equilibrium of the Ising model for d>4. In a first time, we study the thermal behavior in the Extended scaling scheme. By interpolating numerical data in dimensions five to eight, we obtain a development describing the susceptibility in the all high temperature phase. In a second time, we study the finite size effects. The numerical results obtained for the 5d Ising model are compatible with an anomalous growth of the correlation length for free boundary conditions. The subject of the second part is the aging of 2d fully-frustrated spins models. In a first time, we study the aging of the 2d fully-frustrated Ising model during a quench from high temperature to the critical temperature. The presence of topological defects, as the XY model, involves logarithmic corrections during the growth of the correlation length. In a second time, we study aging of the 2d fully-frustrated XY model. During a quench from the ground state to the critical line, aging of spins is well described by spin waves. During a quench from high-temperature to the BKT-temperature for the spins and to the symmetry-breaking temperature of the chiralities, we estimate universal quantities of both variables. The results for chiralities are incompatible with the 2d Ising universality class. Logarithmic corrections are also present.