https://doi.org/10.1140/epjb/e2009-00278-0
Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids
1
Department of Physics, Arizona State University, Tempe, AZ, 85287-1504, USA
2
Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ, 85287-1604, USA
Corresponding author: a ralph.chamberlin@asu.edu
Received:
24
April
2009
Revised:
17
June
2009
Published online:
11
August
2009
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.
PACS: 64.60.an – Finite-size systems / 64.60.F– – Equilibrium properties near critical points, critical exponents / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc) / 75.40.Mg – Numerical simulation studies
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009
