Momentum space renormalization for the sine-Gordon model

Knops, H. J. F.; Ouden, L.W.J. den

doi:10.1016/0378-4371(80)90028-x

Cited by 43 publications

(58 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The advantage of separating the vortex-vortex interaction into a long-distance logarithmic term, accounting for the shortdistance physics through generalized fugacity variables, is that it permits the use of renormalization group (RG) techniques developed for studying the two-dimensional Coulomb gas. 26,28,30 The procedure requires us to consider a generalized version of Eq. (3.2): …”

Section: ṽmentioning

confidence: 99%

See 1 more Smart Citation

Biot-Savart correlations in layered superconductors

2009

View full text Add to dashboard Cite

We discuss the superconductor to normal phase transition in an infinite-layered, type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally-excited pancake vortices and assume the dominant interlayer coupling is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group flow, is that the phase transition in this model is a Kosterlitz-Thouless transition despite being a three-dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence is that the jump in the measured in-plane superfluid stiffness, a universal quantity in 2d KosterlitzThouless theory, receives a small non-universal correction (of order 1% in Bi2Sr2CaCu2O8+x). This overall picture places some claims expressed in the literature on a more secure analytical footing and resolves some conflicting views.

show abstract

Section: ṽmentioning

confidence: 99%

“…In Section III we present an analytical theory of the phase transition using an extension of the 2d momentum shell renormalization group 26 . Accounting for configurations involving stacks of vortices, as discussed above, we re-derive the coupled set of flow equations obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

Biot-Savart correlations in layered superconductors

2009

View full text Add to dashboard Cite

show abstract

“…Now averaging out the short-wavelength components and including the corrections (as in [30]), we finally arrive at an expression for the renormalized mode coupling term, (7) where Λ ∼ 1/a is a suitably chosen upper cut-off with the Green's function G(x, t) given by…”

Section: Dynamic Renormalization and The Results Obtainedmentioning

confidence: 99%

The role of pinning and instability in a class of non-equilibrium growth models

Chattopadhyay

2002

The European Physical Journal B - Condensed Matter

View full text Add to dashboard Cite

1We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behavior. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalization groups) higher ordered nonlinearities have also been discussed. 05.40.+j, 64.60.Ht

show abstract

“…There are two reasons for our pursuing this approach: (i) as anticipated above, in the RG analysis of (3)- (4) a finite (non-zero) surface tension term needs to be allowed for, given that it is generated in any perturbative scheme even if its bare amplitude is zero; (ii) a static renormalization group study of the equilibrium system (4) is ill-defined in some parameter ranges due to divergent integrals [25], similarly to the sG case [8]. Still, the static RG study will provide us, via the appropriate generalization, with the correct expansion of the model non-linearity in terms of relevant operators through the use of Kadanoff's operator product expansion (OPE) [32], as was accomplished in [8,33] for the sG model. In any case, the results to be obtained from the dynamic RG study that follows will also cover the case of a system minimizing both surface area and surface curvature, and will in particular allow us to analyze how the standard sG roughening transition is modified when an additional surface diffusion term is considered.…”

Section: Introductionmentioning

confidence: 99%

“…We additionally provide two appendices. In Appendix A we detail, following [8,33], the OPE which is needed in the dynamic RG in order to perform the appropriate expansion of the lattice potential in (6) into relevant operators. Appendix B closes with a discussion of the specific way in which the roughening transition of the sG model generalizes into that to be obtained in Sec.…”

Section: Introductionmentioning

confidence: 99%

Dynamic renormalization group study of a generalized continuum model of crystalline surfaces

Cuerno

Moro

2001

Phys. Rev. E

View full text Add to dashboard Cite

We apply the Nozières-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential favoring discrete values of the height variable. The model thus interpolates between the overdamped sine-Gordon model and a related continuum model of crystalline tensionless surfaces. The RG flow predicts the existence of an equilibrium roughening transition only for d = 2 dimensional surfaces, between a flat low-temperature phase and a rough high-temperature phase in the Edwards-Wilkinson (EW) universality class. The surface is always in the flat phase for any other substrate dimensions d > 2. For any value of d, the linear surface diffusion mechanism is an irrelevant perturbation of the linear surface tension mechanism, but may induce long crossovers within which the scaling properties of the linear molecular-beam epitaxy equation are observed, thus increasing the value of the sine-Gordon roughening temperature. This phenomenon originates in the non-linear lattice potential, and is seen to occur even in the absence of a bare surface tension term. An important consequence of this is that a crystalline tensionless surface is asymptotically described at high temperatures by the EW universality class.

show abstract

Momentum space renormalization for the sine-Gordon model

Cited by 43 publications

References 8 publications

Biot-Savart correlations in layered superconductors

Biot-Savart correlations in layered superconductors

The role of pinning and instability in a class of non-equilibrium growth models

Dynamic renormalization group study of a generalized continuum model of crystalline surfaces

Contact Info

Product

Resources

About