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Phase transition in a two-dimensional Heisenberg model.

Henk W J Blöte1, Wenan Guo, Henk J Hilhorst

  • 1Faculty of Applied Sciences, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.

Physical Review Letters
|January 22, 2002
PubMed
Summary

We studied the Heisenberg model with nonlinear interactions. For large nonlinearities, a phase transition appears, unlike the standard model, with a jump in correlation length.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Magnetism

Background:

  • The standard two-dimensional classical Heisenberg model (p=1) lacks a phase transition.
  • Nonlinear interactions in similar models, like the XY model, can induce phase transitions.

Purpose of the Study:

  • Investigate the impact of nonlinear nearest-neighbor interactions on the two-dimensional classical Heisenberg model.
  • Determine if and under what conditions a phase transition occurs in this modified model.

Main Methods:

  • Theoretical analysis of the Heisenberg model with a specific nonlinear interaction term V(s,s') = 2K[(1+s x s')/2]p.
  • Comparison with findings for the analogous nonlinear XY model.

Main Results:

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  • The standard Heisenberg model (p=1) exhibits no phase transition.
  • For sufficiently large values of the nonlinearity parameter 'p', a first-order phase transition emerges.
  • Both phases (before and after the transition) display only short-range order.

Conclusions:

  • Nonlinear nearest-neighbor interactions are crucial for inducing phase transitions in the Heisenberg model.
  • A significant jump in correlation length occurs at the first-order transition point.
  • The findings offer insights into the role of interaction nonlinearity in magnetic systems.