Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of shear rates were simulated to test for the predicted invariance, covering both the linear and non-linear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function are identical for state points that are isomorphic. The strain-rate dependence of the viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the non-equilibrium situation of a shear flow, in which the phase diagram is three dimensional because the shear rate defines a third dimension.

The homogeneous plaquette Ising model in two and three dimensions is investigated by means of Monte Carlo simulations. By introducing a suitable order parameter for the two-dimensional lattice, and the finite-size scaling of the corresponding fourth-order cumulant, it is found that, consistent with the previous theoretical indications, the model in two dimensions is disordered at finite temperature and exhibits a zero-temperature phase transition characteristic of the one-dimensional Ising model with an essential (exponential) singularity of the order-parameter susceptibility as opposed to a Curie-law (power-law) divergence. In three dimensions, however, the model is believed to have a first-order phase transition at Tc approximately 3.6 screened by strong metastability leading to a so-called "glassy transition" at T approximately 3.4 when subjected to slow cooling. By computing the configurational entropy Sc identical withS(liquid)-S(crystal) in the supercooled temperature range via thermodynamic integration of the internal energy results, the Kauzmann temperature defined as that temperature where the extrapolated configurational entropy Sc(T) vanishes, is estimated to be TK approximately 3.18 . By finding ways to estimate the equilibration time of the supercooled liquid and the nucleation time of the stable crystal droplets, it is shown that T approximately 3.4 is indeed the limit of stability or the effective spinodal temperature Tsp, at which the two time-scales associated with the quasiequilibration of the supercooled liquid, taueq, and the nucleation of the stable crystal droplets, taunuc, cross one another, with the former rising above the latter such that the supercooled liquid state becomes physically irrelevant below Tsp approximately 3.4 and the impending entropy crisis at TK approximately 3.18 (

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We introduce a bond-diluted Ising model with temperature-dependent concentration of bonds, which is intended to simulate the excitations of bond degrees of freedom as in covalently bonded network liquids arising from the thermal electronic transitions between bonding and antibonding electronic states. The critical behavior of this simplified model system, called the thermalized-bond Ising model, is investigated in terms of the Monte Carlo simulation results of finite-size regular Ising systems, as input for the method of chemical potentials that is generally used to obtain the thermodynamic properties of annealed impurity models. A finite-size scaling analysis of the susceptibility and the fourth-order cumulant results in a reliable estimation of the renormalized critical exponents. The exponents are found to be consistent with the phenomenological renormalization relations, due to Fisher, despite the temperature-dependent bond dilution.

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