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Phase transitions and order in two-dimensional generalized nonlinear σ models.

Tirthankar Banerjee1, Niladri Sarkar1,2, Abhik Basu1

  • 1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 700064, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2016
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Summary
This summary is machine-generated.

We explore unusual phase transitions in generalized nonlinear sigma models (NLS) with added degrees of freedom. These models exhibit novel stiff and soft phases in 2D, impacting spin stiffness and fluctuations differently than pure NLS.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Classical generalized O(N) nonlinear sigma models (NLS) are fundamental for studying systems with continuous symmetries.
  • Understanding phase transitions and order in low-dimensional systems is crucial for various scientific fields.
  • Pure NLS models exhibit specific behaviors in phase transitions, particularly in two dimensions (2D).

Purpose of the Study:

  • To investigate novel phase transitions in generalized O(N) nonlinear sigma models.
  • To analyze the nature of order and spin stiffness in these modified models.
  • To compare the behavior of these models with pure NLS, especially in 2D.

Main Methods:

  • Construction of generalized NLS models by coupling pure NLS with Ising spins, advective Stokesian velocity, or multiplicative noises.
  • Analysis of phase transitions by examining the behavior of effective spin stiffness in the long wavelength limit.
  • Calculation of fluctuation variances and spin-spin correlations in the thermodynamic limit.

Main Results:

  • Unusual phase transitions between stiff and soft phases are identified in 2D for models with Ising spins, advective velocity, and short-ranged multiplicative noise.
  • In the stiff phase, transverse spin fluctuation variance scales as lnlnL in 2D, weaker than the lnL of quasi-long-range order.
  • For N=2 in 2D, spin-spin correlations decay logarithmically, with exponents dependent on model parameters.

Conclusions:

  • The introduced degrees of freedom fundamentally alter phase transition behavior compared to pure NLS.
  • The findings reveal new mechanisms for controlling order and stiffness in low-dimensional systems.
  • Results offer insights into equilibrium and nonequilibrium phase transitions in systems with continuous symmetries.