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

Maddalena Venturoli, Eric Vanden Eijnden, Giovanni Ciccotti

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)188-222
Number of pages35
JournalJournal of Mathematical Chemistry
Volume45
Issue number1
DOIs
StatePublished - Jan 2009

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Ising model
Ising Model
Phase Transition
Phase Transformation
Strings
Kinetics
Phase transitions
Free Energy
Free energy
Transition State
Periodic Systems
Approximation
External Field
Time varying systems
State Space
Boundary conditions
Path

Keywords

  • Ising model
  • Minimum free energy path
  • Phase transition
  • Sampling
  • String method

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Kinetics of phase transitions in two dimensional Ising models studied with the string method. / Venturoli, Maddalena; Vanden Eijnden, Eric; Ciccotti, Giovanni.

In: Journal of Mathematical Chemistry, Vol. 45, No. 1, 01.2009, p. 188-222.

Research output: Contribution to journalArticle

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