Thermodynamics of the two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="italic">XY</mml:mi></mml:mrow></mml:math>model from functional renormalization

Jakubczyk, P.; Eberlein, Andreas

doi:10.1103/physreve.93.062145

Cited by 22 publications

(18 citation statements)

References 53 publications

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“…Both of these intervals of values are reasonably compatible with our estimate of T c 1.03. Last but not least, the peak of specific heat that we report at T 1.03 is in agreement with old and recent findings in references [35][36][37]39].…”

Section: Numerical Evidence Of the Kt Phase Transitionsupporting

confidence: 93%

Geometrical and topological study of the Kosterlitz–Thouless phase transition in the XY model in two dimensions

Bel-Hadj-Aissa¹,

Gori²,

Franzosi³

et al. 2021

J. Stat. Mech.

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Phase transitions do not necessarily correspond to a symmetry-breaking phenomenon. This is the case of the Kosterlitz–Thouless (KT) phase transition in a two-dimensional classical XY model, a typical example of a transition stemming from a deeper phenomenon than a symmetry-breaking. Actually, the KT transition is a paradigmatic example of the successful application of topological concepts to the study of phase transition phenomena in the absence of an order parameter. Topology conceptually enters through the meaning of defects in real space. In the present work, the same kind of KT phase transition in a two-dimensional classical XY model is tackled by resorting again to a topological viewpoint, however focussed on the energy level sets in phase space rather than on topological defects in real space. Also from this point of view, the origin of the KT transition can be attributed to a topological phenomenon. In fact, the transition is detected through peculiar geometrical changes of the energy level sets which, after a theorem in differential topology, are direct probes of topological changes of these level sets.

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Section: Numerical Evidence Of the Kt Phase Transitionsupporting

confidence: 93%

Geometrical and topological study of the Kosterlitz–Thouless phase transition in the XY model in two dimensions

Bel-Hadj-Aissa¹,

Gori²,

Franzosi³

et al. 2021

J. Stat. Mech.

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“…For the KT transition [(d, N ) = (2, 2)], the (complete) DE at order ∂ 2 was addressed in Refs. [28,29,31]. The flow equations solved in the present paper are equivalent to those analyzed therein at the fixed point.…”

Section: Dimensionality D =mentioning

confidence: 93%

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Chlebicki

Jakubczyk

2021

SciPost Phys.

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We employ the functional renormalization group framework at the second order in the derivative expansion to study the O(N)O(N) models continuously varying the number of field components NN and the spatial dimensionality dd. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents \nuν and \etaη across a line in the (d,N)(d,N) plane, which passes through the point (2,2)(2,2). By direct numerical evaluation of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the (d,N)(d,N) plane, however no evidence of discontinuous or singular first and second derivatives of these functions for d>2d>2. The computed derivatives of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) become increasingly large for d\to 2d→2 and N\to 2N→2 and it is only in this limit that \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on NN for d>2d>2 we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality dd approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

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“…Our approach is based on the nonperturbative renormalization-group approach (NPRG) and, contrary to most previous works, does not introduce vortices explicitly. While only a refined approximation scheme of the NPRG equations is able to capture all features of the KT transition and in particular the low-temperature line of fixed points, [29][30][31][32] we shall use a simple approximation 33,34 which is easily numerically tractable even in the quasi-2D case. In this approximation, the KT transition is not captured stricto sensu since the correlation length is always finite.…”

Section: Introductionmentioning

confidence: 99%

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

Rançon

Dupuis

2017

Phys. Rev. B

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We study the quasi-two-dimensional quantum O(2) model, a quantum generalization of the Lawrence-Doniach model, within the nonperturbative renormalization-group approach and propose a generic phase diagram for layered three-dimensional systems with an O(2)-symmetric order parameter. Below the transition temperature we identify a wide region of the phase diagram where the renormalization-group flow is quasi-two-dimensional for length scales smaller than a Josephson length lJ , leading to signatures of Kosterlitz-Thouless physics in the temperature dependence of physical observables. In particular the order parameter varies as a power law of the interplane coupling with an exponent which depends on the anomalous dimension (itself related to the stiffness) of the strictly two-dimensional low-temperature Kosterlitz-Thouless phase. arXiv:1710.01000v2 [cond-mat.stat-mech]

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Thermodynamics of the two-dimensionalXYmodel from functional renormalization

Cited by 22 publications

References 53 publications

Geometrical and topological study of the Kosterlitz–Thouless phase transition in the XY model in two dimensions

Geometrical and topological study of the Kosterlitz–Thouless phase transition in the XY model in two dimensions

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

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