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

Solid State and Materials

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.

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 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of PhysicsArizona State UniversityTempeUSA
  2. 2.Department of Chemistry and BiochemistryArizona State UniversityTempeUSA

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