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We investigate the calorimetric liquid-glass transition by performingsimulations of a binary Lennard-Jones mixture in one through four dimensions.Starting at a high temperature, the systems are cooled to T=0 and heated backto the ergodic liquid state at constant rates. Glass transitions are observedin two, three and four dimensions as a hysteresis between the cooling andheating curves. This hysteresis appears in the energy and pressure diagrams,and the scanning-rate dependence of the area and height of the hysteresis canbe described by power laws. The one dimensional system does not experience aglass transition but its specific heat curve resembles the shape of the $D\geq2$ results in the supercooled liquid regime above the glass transition. As $D$increases, the radial distribution functions reflect reduced geometricconstraints. Nearest-neighbor distances become smaller with increasing $D$ dueto interactions between nearest and next-nearest neighbors. Simulation data forthe glasses are compared with crystal and melting data obtained with aLennard-Jones system with only one type of particle and we find that withincreasing $D$ crystallization becomes increasingly more difficult.

Glass transitions in 1, 2, 3, and 4 dimensional binary Lennard-Jones systems