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Transient backbending behavior in the Ising model with fixed magnetization.

F Gulminelli1, J M Carmona, Ph Chomaz

  • 1LPC Caen (IN2P3-CNRS/ISMRA et Université), F-14050 Caen Cédex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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The Ising model with fixed magnetization reveals that backbending in finite systems indicates the transition order, even in small systems. This behavior is transient and does not converge to a plateau in the thermodynamic limit.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Backbending phenomena in equations of state for finite systems are not fully understood.
  • The Ising model with fixed magnetization (IMFM) provides a framework to study these anomalies.

Purpose of the Study:

  • To investigate the physical origin of backbending in the equations of state for finite systems.
  • To determine if the order of a thermodynamic transition can be identified in finite systems.

Main Methods:

  • Analysis of topological properties of observable distributions.
  • Examination of the largest cluster's behavior with increasing lattice size.
  • Study of convexity anomalies in the IMFM thermodynamic potential.

Main Results:

Related Experiment Videos

  • The order of the transition at the thermodynamic limit is recognizable in finite systems, irrespective of lattice size.
  • Backbending in the caloric curve appears to be a transient behavior.
  • A first-order transition is still indicated by a discontinuity in the magnetization equation of state.

    • Conclusions:

    • Finite systems can exhibit characteristics of thermodynamic transitions observable at the thermodynamic limit.
    • Backbending in caloric curves is a finite-size effect that does not persist in the thermodynamic limit.
    • The IMFM framework successfully identifies transition orders in finite systems.