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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tirthankar BanerjeeAbhik Basu

Abstract

We study phase transitions and the nature of order in a class of classical generalized O(N) nonlinear σ models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising ferromagnetic spins, (ii) an advective Stokesian velocity, and (iii) multiplicative noises. In examples (i) and (ii), and also (iii) with the associated multiplicative noise being not sufficiently long-ranged, we show that the models may display a class of unusual phase transitions between stiff and soft phases, where the effective spin stiffness respectively diverges and vanishes in the long wavelength limit at two dimensions (2D), unlike in pure NLS. In the stiff phase, in the thermodynamic limit the variance of the transverse spin (or, the Goldstone mode) fluctuations are found to scale with the system size L in 2D as lnlnL with a model-dependent amplitude, which is markedly weaker than the well-known lnL dependence of the variance of the broken symmetry modes in models that display quasi-long-range order in 2D. Equivalently, for N=2 at 2D the equal-time spin-spin correlations decay in powers of inverse logarithm of the spatial separation with model-dependent exponents. These transitions are controlled by the...Continue Reading

References

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Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tirthankar Banerjee, Abhik Basu

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Citations

Sep 28, 2017·Physical Review. E·Tirthankar Banerjee, Abhik Basu

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