High-Moment-Low-Moment Description of Magnetovolume Effects in Y(Mn x Al 1− x ) 2 and Y x Sc 1− x Mn 2
Based on the assumption of a high-moment-low-moment instability of the Mn atom, we construct a simple spin model with coupled magnetic and spatial degrees of freedom to describe the Laves phase systems Y(Mn x Al 1 m x ) 2 and Y x Sc 1 m x Mn 2 . Monte Carlo simulations of this model qualitatively reproduce anomalies observed in these materials like a discontinuous giant volume change and anomalous thermal expansion behavior.
Monte Carlo simulations of magnetovolume instabilities in anti-Invar systems
We perform constant pressure Monte Carlo simulations of a spin-analogous model which describes coupled spatial and magnetic degrees of freedom on an fcc lattice. Our calculations qualitatively reproduce magnetovolume effects observed in some rare earth manganese compounds, especially in the anti-Invar material YMn2. These are a sudden collapse of the magnetic moment which is connected with a huge volume change, and a largely enhanced thermal expansion coefficient.
Multi-Dimensional Utility and the Index Number Problem: Jeremy Bentham, J. S. Mill, and Qualitative Hedonism
This article develops an unconventional perspective on the utilitarianism of Bentham and Mill in at least four areas. First, it is shown that both authors conceived of utility as irreducibly multi-dimensional, and that Bentham in particular was very much aware of the ambiguity that multi-dimensionality imposes upon optimal choice under the greatest happiness principle. Secondly, I argue that any attribution of intrinsic worth to any form of human behaviour violates the first principles of Bentham's and Mill's utilitarianism, and that this renders both authors immune to the claim by G. E. Moore that they committed a ‘naturalistic fallacy’. Thirdly, in light of these contentions, I find no flaw in Mill's ‘proof of utility’. Fourthly, I use the notion of intrapersonal utility weights to provide an interpretation of Mill's qualitative hedonism that is entirely consistent with his value monism.