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

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2009-09, Vol.71 (1), p.1-6
• Main Authors: Chamberlin, R. V., Vermaas, J. V., Wolf, G. H.
• Format: Article
• Language: English
• Subjects: Complex Systems; Condensed Matter Physics; Exact sciences and technology; Fluid- and Aerodynamics; Phase transitions: general studies; Physics; Physics and Astronomy; Solid State and Materials; Solid State Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Thermodynamics
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2009-00278-0

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.