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PHYSICAL REVIEW E 85, 021135 (2012) Geometrical properties of the Potts model during the coarsening regime
 

Summary: PHYSICAL REVIEW E 85, 021135 (2012)
Geometrical properties of the Potts model during the coarsening regime
Marcos P. O. Loureiro,1
Jeferson J. Arenzon,2
and Leticia F. Cugliandolo1
1
Universit´e Pierre et Marie Curie-Paris VI, LPTHE UMR 7589, 4 Place Jussieu, FR-75252 Paris Cedex 05, France
2
Instituto de F´isica and INCT Sistemas Complexos, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre,
Rio Grande do Sul, Brazil
(Received 11 December 2011; published 23 February 2012)
We study the dynamic evolution of geometric structures in a polydegenerate system represented by a q-state
Potts model with nonconserved order parameter that is quenched from its disordered into its ordered phase. The
numerical results obtained with Monte Carlo simulations show a strong relation between the statistical properties
of hull perimeters in the initial state and during coarsening: The statistics and morphology of the structures that
are larger than the averaged ones are those of the initial state, while the ones of small structures are determined
by the curvature-driven dynamic process. We link the hull properties to the ones of the areas they enclose. We
analyze the linear von Neumann-Mullins law, both for individual domains and on the average, concluding that
its validity, for the later case, is limited to domains with number of sides around 6, while presenting stronger
violations in the former case.

  

Source: Arenzon, Jeferson J. - Instituto de Física, Universidade Federal do Rio Grande do Sul

 

Collections: Physics