PMID- 26764658
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20160830
LR  - 20160115
IS  - 1550-2376 (Electronic)
IS  - 1539-3755 (Linking)
VI  - 92
IP  - 6
DP  - 2015 Dec
TI  - Phase transitions and order in two-dimensional generalized nonlinear sigma models.
PG  - 062133
LID - 10.1103/PhysRevE.92.062133 [doi]
AB  - We study phase transitions and the nature of order in a class of classical 
      generalized O(N) nonlinear sigma 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 model 
      parameters those couple the O(N) spins with the additional variables. In the 
      presence of long-range noises in example (iii), true long-range order may set in 
      2D, depending upon the specific details of the underlying dynamics. Our results 
      should be useful in understanding phase transitions in equilibrium and 
      nonequilibrium low-dimensional systems with continuous symmetries in general.
FAU - Banerjee, Tirthankar
AU  - Banerjee T
AD  - Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 
      700064, India.
FAU - Sarkar, Niladri
AU  - Sarkar N
AD  - Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 
      700064, India.
AD  - Max-Planck Institut fur Physik Komplexer Systeme, Nothnitzer Str. 38, Dresden, 
      D-01187 Germany.
FAU - Basu, Abhik
AU  - Basu A
AD  - Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 
      700064, India.
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
DEP - 20151218
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
EDAT- 2016/01/15 06:00
MHDA- 2016/01/15 06:01
CRDT- 2016/01/15 06:00
PHST- 2015/08/10 00:00 [received]
PHST- 2016/01/15 06:00 [entrez]
PHST- 2016/01/15 06:00 [pubmed]
PHST- 2016/01/15 06:01 [medline]
AID - 10.1103/PhysRevE.92.062133 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062133. doi: 
      10.1103/PhysRevE.92.062133. Epub 2015 Dec 18.