P L Krapivsky 2004 J. Phys. A: Math. Gen. 37 6917 doi:10.1088/0305-4470/37/27/004
Dynamical critical behaviours of the Ising spin chain: Swendsen–Wang and Wolff algorithms
P L Krapivsky
Show affiliationsWe study the zero-temperature Ising chain evolving according to the Swendsen–Wang dynamics. We determine analytically the domain length distribution and various 'historical' characteristics, e.g. the density of unreacted domains is shown to scale with the average domain length as 
l
−δ with δ = 3/2 (for the q-state Potts model, δ = 1 + q−1). We also compute the domain length distribution for the Ising chain endowed with the zero-temperature Wolff dynamics.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.30.Hq Ordinary differential equations
- MSC
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65Nxx Partial differential equations, boundary value problems
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
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Issue 27 (9 July 2004)
Received 2 April 2004, in final form 20 May 2004
Published 22 June 2004
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Dynamical critical behaviours of the Ising spin chain: Swendsen–Wang and Wolff algorithms
P L Krapivsky 2004 J. Phys. A: Math. Gen. 37 6917
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