Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann's scenario of a `lower metastability limit' of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation-dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.Comment: 25 page

Mortality Contingent Claims, Health Care, and Social Insurance

This paper analyzes the savings and health care impacts of mortality contingent claims, defined here as income measures, such as annuities and life-insurance, under which earned income is contingent on the length of one's life. The postwar increase in mandatory annuity and life-insurance programs, as well as the rapid increase in life-expectancy, motivates a better understanding of the effects that mortality contingent claims have on resources devoted to life-extension. We analyze the incentives that such claims imply for life-extension when resources may affect mortality endogenously and argue that these incentives dramatically alter the standard conclusions obtained when mortality is treated exogenously.