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The shear modulus G of two glass-forming colloidal model systems in d=3 andd=2 dimensions is investigated by means of, respectively, molecular dynamicsand Monte Carlo simulations. Comparing ensembles where either the shear straingamma or the conjugated (mean) shear stress tau are imposed, we compute G fromthe respective stress and strain fluctuations as a function of temperature Twhile keeping a constant normal pressure P. The choice of the ensemble is seento be highly relevant for the shear stress fluctuations mu_F(T) which atconstant tau decay monotonously with T following the affine shear elasticitymu_A(T), i.e. a simple two-point correlation function. At variance,non-monotonous behavior with a maximum at the glass transition temperature T_gis demonstrated for mu_F(T) at constant gamma. The increase of G below T_g isreasonably fitted for both models by a continuous cusp singularity, G(T) isproportional to (1-T/T_g)^(1/2), in qualitative agreement with some recentreplica calculations. It is argued, however, that longer sampling times maylead to a sharper transition. The additive jump discontinuity predicted bymode-coupling theory and other replica calculations thus cannot ultimately beruled out.

Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time