Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids

Abstract

The Boltzmann factor comes from the linear change in entropy of an infinite heat bath during a local fluctuation; small systems have significant nonlinear terms. We present theoretical arguments, experimental data, and Monte-Carlo simulations indicating that nonlinear terms may also occur when a particle interacts directly with a finite number of neighboring particles, forming a local region that fluctuates independent of the infinite bath. A possible mechanism comes from the net force necessary to change the state of a particle while conserving local momentum. These finite-sized local regions yield nonlinear fluctuation constraints, beyond the Boltzmann factor. One such fluctuation constraint applied to simulations of the Ising model lowers the energy, makes the entropy extensive, and greatly improves agreement with the corrections to scaling measured in ferromagnetic materials and critical fluids.

21 pages, 4 figures

References in corpus (5)

• Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series
• Extended Scaling for Ferromagnets
• Master crossover functions for the one-component fluid "subclass"
• A free-energy landscape picture and Landau theory for the dynamics of disordered materials
• Fluctuation-theory constraint for extensive entropy in Monte-Carlo simulations

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• Fluctuation theorems and 1/f noise from a simple matrix
• Critical scaling to infinite temperature
• Modified Bose-Einstein and Fermi-Dirac statistics if excitations are localized on an intermediate length scale: Application to non-Debye specific heat
• Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior