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
N1 - Funding Information:
Acknowledgements One of the authors (M.V.) was supported by the EC through the Marie Curie EST project MEST-CT-2005-020491, by CECAM (Lyon) and by US DARPA grant 25-74200-F6053. Part of this work was performed while one of the authors (M.V.) was a researcher at CECAM. We acknowledge CECAM for providing the computational resources used for this work.
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
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U2 - 10.1007/s10910-008-9376-5
DO - 10.1007/s10910-008-9376-5
M3 - Article
AN - SCOPUS:57849108039
SN - 0259-9791
VL - 45
SP - 188
EP - 222
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 1
ER -