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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Published on: September 26, 2016

Universality class of the pair contact process with diffusion.

F Smallenburg1, G T Barkema

  • 1Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary

The pair contact process with diffusion (PCPD) shows inconsistent critical exponent estimates. Using a specific density combination resolves this, aligning PCPD with directed percolation (DP) universality class.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • The pair contact process with diffusion (PCPD) is a model system for studying phase transitions.
  • Standard analysis methods for PCPD simulations often yield conflicting results for critical exponents.

Purpose of the Study:

  • To investigate the pair contact process with diffusion (PCPD) using computational simulations.
  • To obtain consistent estimates for critical exponents in PCPD.
  • To determine the universality class of PCPD.

Main Methods:

  • Utilizing standard Monte Carlo simulations.
  • Performing simulations at fixed densities.
  • Analyzing simulation results using particle and pair densities, and a specific linear combination thereof.

Main Results:

  • Standard analysis of particle and pair densities led to inconsistent critical exponent estimates.
  • A refined analysis using a specific linear combination of densities suppressed corrections and yielded consistent estimates: delta=0.16(2), beta=0.28(2), and z=1.58.
  • The obtained critical exponents are consistent with those of directed percolation (DP).

Conclusions:

  • The pair contact process with diffusion (PCPD) falls within the same universality class as directed percolation (DP).
  • A carefully chosen analysis method is crucial for accurate critical exponent determination in PCPD.