Random symmetry-breaking fields and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>model

Cardy, John; Östlund, Stellan

doi:10.1103/physrevb.25.6899

Cited by 227 publications

(334 citation statements)

References 21 publications

Supporting

Mentioning

320

Contrasting

Unclassified

Order By: Relevance

“…The studied system is known in physics as the mean-field theory for the random-field XY model, [11]. In [10] it is proven that the system exhibits a jump bifurcation and hysteresis as K is varied.…”

Section: Particle Modelmentioning

confidence: 99%

Dynamics of Decision Making in Animal Group Motion

et al. 2009

View full text Add to dashboard Cite

We present a continuous model of a multi-agent system motivated by simulation studies on dynamics of decision making in animal groups in motion. Each individual moves at constant speed in the plane and adjusts its heading in response to relative headings of others in the population. Two subgroups of the population are informed such that individuals in each subgroup have a preferred direction of motion. The model exhibits fast and slow time scales allowing for a reduction in the dimension of the problem. The stable solutions for the reduced model correspond to compromise by individuals with conflicting preferences. We study the global phase space for the proposed reduced model by computing equilibria and proving stability and bifurcations.

show abstract

Section: Particle Modelmentioning

confidence: 99%

Dynamics of Decision Making in Animal Group Motion

et al. 2009

View full text Add to dashboard Cite

show abstract

“…However, it should be emphasized again that we have not found a clear-cut separation of the random vector potential and random mass parts of the disorder at the lattice level. We, therefore, have to rely on the results of a different field-theoretic RG analysis 7,9 when discussing how the two types of randomness flow and affect each other ͑note that a similar somewhat heuristic argument was used in Ref. 20 to obtain crossover scales in the vortex glass problem͒.…”

Section: B On the Origin Of Statesmentioning

confidence: 99%

“…Finally, it is useful to note that these bipartite problems are closely related to a well-studied vortex glass problem. [7][8][9] The field-theoretic analyses that lead to these predictions, however, do not provide a direct physical picture of the origin of the divergent DOS at the band center and the nature of the low-energy states. Developing such a picture is the main thrust of the present paper.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Particle-hole symmetric localization in two dimensions

2002

View full text Add to dashboard Cite

We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states (E) at the band center Eϭ0. The most general system of this kind ͓R. Gade, Nucl. Phys. B 398, 499 ͑1993͔͒ exhibits critical behavior and has (E) that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. ͓Phys. Rev. B 50, 7526 ͑1994͔͒ has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder-this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ''surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is (E)ϳE Ϫ1 e Ϫc͉ln E͉ 2/3 , different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ''string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.

show abstract

“…One phase (P SL g ) has a line of fixed points related to P SL(1|1) studied in [24], and appears to be the only massless phase. It is in the same universality class as dense polymers and is also closely related to the disordered XY model [25]. A sigma model version of this theory was proposed by Zirnbauer in connection with the quantum Hall transition [41], based on the work [45] [46].…”

Section: Introductionmentioning

confidence: 99%

Strong-coupling fixed points of current interactions and disordered fermions in two dimensions

LeClair

2001

Phys. Rev. B

View full text Add to dashboard Cite

The all-orders βeta function is used to study disordered Dirac fermions in 2D. The generic strong coupling fixed 'points' of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to subalgebras of the maximal current algebra at short distances. We argue that IR fixed point theories are generally current algebra cosets. We illustrate this with the simple example of anisotropic su(2), which is the physics of Kosterlitz-Thouless transitions. We propose a phase diagram for the ChalkerCoddington network model which is in the universality class of the integer Quantum Hall transition. One phase is in the universality class of dense polymers.Typeset using REVT E X * Laboratoire associé No. 280 au CNRS 1

show abstract

Random symmetry-breaking fields and theXYmodel

Cited by 227 publications

References 21 publications

Dynamics of Decision Making in Animal Group Motion

Dynamics of Decision Making in Animal Group Motion

Particle-hole symmetric localization in two dimensions

Strong-coupling fixed points of current interactions and disordered fermions in two dimensions

Contact Info

Product

Resources

About