### 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 language | English (US) |
---|---|

Pages (from-to) | 188-222 |

Number of pages | 35 |

Journal | Journal of Mathematical Chemistry |

Volume | 45 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2009 |

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### Keywords

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

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*45*(1), 188-222. https://doi.org/10.1007/s10910-008-9376-5

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

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 45, no. 1, pp. 188-222. https://doi.org/10.1007/s10910-008-9376-5

}

TY - JOUR

T1 - Kinetics of phase transitions in two dimensional Ising models studied with the string method

AU - Venturoli, Maddalena

AU - Vanden Eijnden, Eric

AU - Ciccotti, Giovanni

PY - 2009/1

Y1 - 2009/1

N2 - 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.

AB - 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.

KW - Ising model

KW - Minimum free energy path

KW - Phase transition

KW - Sampling

KW - String method

UR - http://www.scopus.com/inward/record.url?scp=57849108039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57849108039&partnerID=8YFLogxK

U2 - 10.1007/s10910-008-9376-5

DO - 10.1007/s10910-008-9376-5

M3 - Article

AN - SCOPUS:57849108039

VL - 45

SP - 188

EP - 222

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 1

ER -