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Surface and bulk transitions in three-dimensional O(n) models.

Youjin Deng1, Henk W J Blöte, M P Nightingale

  • 1Laboratory for Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study explores surface criticality in O(n) models, including Ising, XY, and Heisenberg models, using Monte Carlo simulations. Researchers determined critical couplings and surface exponents, finding evidence for special surface transitions in all models.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Surface criticality in statistical models is crucial for understanding phase transitions at interfaces.
  • The O(n) models provide a versatile framework to study diverse magnetic systems.

Purpose of the Study:

  • To investigate surface criticality in the O(n) models (Ising, XY, Heisenberg) on a simple-cubic lattice.
  • To determine critical couplings and surface exponents for ordinary and special transitions.
  • To explore finite-size corrections and the existence of special surface transitions.

Main Methods:

  • Monte Carlo simulations
  • Finite-size scaling analysis
  • Simulation of models with open surfaces

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Main Results:

  • Calculated critical couplings for n=2 and n=3.
  • Determined surface magnetic exponents at the ordinary transition for n=1, 2, and 3.
  • Located special transition points for Ising and XY models and found exponents for surface thermal and magnetic transitions.
  • Observed finite-size corrections with an exponent near -1/2.
  • Found substantial evidence for a special surface transition in the Heisenberg model.

Conclusions:

  • The study provides precise values for critical couplings and surface exponents for the Ising, XY, and Heisenberg models.
  • Evidence supports the existence of special surface transitions in these models, contributing to the understanding of surface phenomena in statistical mechanics.