We present a simulation study of how properties of symmetric diblock copolymers depend on the invariant degree of polymerization (N) over bar, focusing on the vicinity of the orderdisorder transition (ODT). Results from several coarse-grained simulation models are combined to cover a range of (N) over bar similar or equal to 200-8000 that includes most of the experimentally relevant range. Results are presented for the free energy per chain, the value of Chi N-e at the ODT, the latent heat of transition, the layer spacing, the composition profile, and compression modulus in the ordered phase. Universality (i.e., model independence) is demonstrated by showing that equivalent results for all properties are obtained from corresponding thermodynamic states of different simulation models. Corresponding states of symmetric copolymers are states with equal values of the parameters XeN and (N) over bar, where X-e is an effective FloryHuggins interaction parameter and N is a degree of polymerization. The underlying universality becomes apparent, however, only if data are analyzed using an adequate estimate of X-e, which we obtain by fitting the structure factor in the disordered state to recent theoretical predictions. The results show that behavior near the ODT exhibits a different character at moderate and high values of (N) over bar, with a crossover near (N) over bar similar or equal to 10(4). Within the range (N) over bar similar or equal to 10(4) studied here, the ordered and disordered phases near the ODT both contain strongly segregated domains of nearly pure A and B, in contrast to the assumption of weak segregation underlying the FredricksonHelfand (FH) theory. In this regime, the FH theory is inaccurate and substantially underestimates the value of x(e)N at the ODT. Results for the highest values of (N) over bar studied here agree reasonably well with FH predictions, suggesting that the theory may be accurate for (N) over bar similar or equal to 10(4). Self-consistent field theory (SCFT) grossly underestimates (XeN)ODT for modest (N) over bar because it cannot describe strong correlations in the disordered phase. SCFT is found, however, to yield accurate predictions for several properties of the ordered lamellar phase.