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Journal of Physics Conference Series

Short-time behavior of percolation observables at O(3) spin models: a preliminary analysis

Wanderson Gonçalves Wanzeller

Published Mar 11, 2014• 0 citations
Publisher

Abstract

We analyzed the short-time behavior of percolation observables at three dimensional O(3) spin models. Following the Metropolis time evolution we can compare the magnetic and percolation order parameters. The magnetic order parameter evolves with a power law M ∼ t θ , as expected. However the percolation order parameter follows a different law. We explored this particularity and raised some hypothesis. This paper is a preliminar analysis on this subject.

DOI
10.1088/1742-6596/487/1/012009

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We analyzed the short-time behavior of percolation observables at three dimensional O(3) spin models. Following the Metropolis time evolution we can compare the magnetic and percolation order parameters. The magnetic order parameter evolves with a power law M ∼ t θ , as expected. However the percolation order parameter follows a different law. We explored this particularity and raised some hypothesis. This paper is a preliminar analysis on this subject.
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We present results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte Carlo) short-time evolution of the system with small initial magnetization and heat-bath dynamics. We find qualitatively different dynamic behaviors for the magnetization M and for omega, the so-called strength of the percolating cluster, which is the order parameter of the percolation transition. More precisely, we obtain a (leading) exponential form for omega as a function of the Monte Carlo time t, to be compared with the power-law increase encountered for M at short times. Our results suggest that, although the descriptions in terms of magnetic or percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times.
Abstract. We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Ω, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables.
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We examine the average cluster distribution as a function of lattice probability for a very small (L=6)(L=6)(L=6) lattice and determine the scaling function of three-dimensional percolation. The behavior of the second moment, calculated from the average cluster distribution of L=6L=6L=6 and L=63L=63L=63 lattices, is compared to power-law behavior predicted by the scaling function. We also examine the finite-size scaling of the critical point and the size of the largest cluster at the critical point. This analysis leads to estimates of the critical exponent $\ensuremath{\nu}$ and the ratio of critical exponents $\ensuremath{\beta}/\ensuremath{\nu}$.