Journal of Mathematical Chemistry

, Volume 45, Issue 1, pp 188–222 | Cite as

Kinetics of phase transitions in two dimensional Ising models studied with the string method

  • Maddalena Venturoli
  • Eric Vanden-Eijnden
  • Giovanni Ciccotti
Original Paper


The kinetics of phase transitions in the two dimensional Ising model under different conditions is studied using the string method. The key idea is to work in collective variables, consisting of block of spins, which allow for a continuous approximation of the collective variable state-space. The string method computes the minimum free energy path (MFEP) in this collective variable space, which is shown to explain the mechanism of the phase transformation (in particular, an approximation of its committor function, its free energy and its transition state). In this paper the theoretical background of the technique as well as its computational aspects are discussed in details. The string method is then used to analyze phase transition in the Ising model with imposed boundary conditions and in a periodic system under an external field of increasing magnitude. In each case, the mechanism of the phase transformation is elucidated.


Minimum free energy path String method Sampling Phase transition Ising model 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Maddalena Venturoli
    • 1
  • Eric Vanden-Eijnden
    • 1
  • Giovanni Ciccotti
    • 2
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Dipartimento di Fisica and CNISMUnità di Roma 1, Università di Roma La SapienzaRomaItaly

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