Approximate scale invariance in particle systems: a large-dimensional justification

Abstract

Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of temperatures and densities. In a recent series of works, it has been argued that such correspondences hold to a surprisingly good approximation in a much more general class of potentials, an observation that summarizes many properties that have been observed in the past. In this paper we show that such relations are exact in high-dimensional liquids and glasses, a limit in which the conditions for these mappings to hold become transparent. The special role played by the exponential potential is also confirmed.

11 pages, 3 figures -- New version includes added discussions, figures and references, as well as an appendix about the derivation of equations

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Cited by in corpus (11)

• Active hard-spheres in infinitely many dimensions
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• The EXP pair-potential system. II. Fluid phase isomorphs
• The EXP pair-potential system. I. Fluid phase isotherms, isochores, and quasiuniversality
• An extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain
• Density scaling of generalized Lennard-Jones fluids in different dimensions
• Characterizing nonaffinity upon decompression of soft-sphere packings
• Comparing zero-parameter theories for the WCA and harmonic-repulsive melting lines
• Theory of Generalized Hertzian Hyperspheres
• Variation along liquid isomorphs of the driving force for crystallization