Equilibrium and quenched energy distributions for spin glasses

In the four-dimensional Edwards-Anderson +/-J spin glasses, we observe that the quenched energies distribution from T = 2.5 are similar to those observed for the equilibrium states at T = 1.0. We show that although these states appear close there are subtle differences which are only seen when we try to quench the system from T = 2.5 for a longer number of Monte Carlo steps. The T = 2.5 states do not evolve to those seen for the states quenched from T = 1.0. We try to identify regions responsible for the subtle differences.