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

TL;DR

This paper explores nonlinear fluctuation effects beyond the traditional Boltzmann factor in finite local regions of ferromagnetic materials and critical fluids, supported by theory, experiments, and simulations.

Contribution

It introduces a new framework for nonlinear fluctuation constraints that improve the understanding of corrections to scaling in critical phenomena.

Findings

Nonlinear fluctuation terms can occur in finite local regions.

Applying these constraints improves simulation accuracy.

Enhanced agreement with experimental data on ferromagnetic 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.