Multicritical behaviour in the fully frustrated<i>XY</i>model and related systems

Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore

doi:10.1088/1742-5468/2005/12/p12002

Cited by 100 publications

(121 citation statements)

References 121 publications

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“…Such fractional vortices are found for many models from the class of the Ising-O(2) model: the fully frustrated XY model 36,37 , XY antiferromagnet on a triangular lattice 38 , XY helimagnets 39,40 , etc. The second scenario when two transitions coincide is also observed in the Ising-XY model [41][42][43][44][45] and XY J 1 -J 3 model on a square lattice 46 . (The N = 3 case of the last model is considered in the current study, see the description of the model below.)…”

Section: Korshunov Arguedmentioning

confidence: 66%

First-order transition induced by topological defects in theO(3)principal chiral model

Сорокин

2017

Phys. Rev. B

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Using Monte Carlo simulations, we study thermal and critical properties of two systems, in which domain walls and so-called Z2-vortices as topological defects are presented. The main model is a lattice version of the O(3) principal chiral model. We find a first order transition and give qualitative arguments that the first order is induced by topological defects. We also consider the model of frustrated antiferromagnet on a square lattice with the additional exchange interaction between spins of the third range order. This model belongs to the same symmetry class. In this model, a transition is of first order too.

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Section: Korshunov Arguedmentioning

confidence: 66%

First-order transition induced by topological defects in theO(3)principal chiral model

Сорокин

2017

Phys. Rev. B

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“…This would suggest a first-order transition. It is also possible that more than one transition is present, each of them associated to a partial decoupling of some degrees of freedom, hence to a different symmetry-breaking pattern, as it happens in two-dimensional frustrated XY models [45]. In this case, continuous transition would still be possible.…”

Section: Resultsmentioning

confidence: 99%

Three-dimensional antiferromagneticCPN−1models

2015

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We investigate the critical behavior of three-dimensional antiferromagnetic CP N−1 (ACP N−1 ) models in cubic lattices, which are characterized by a global U(N ) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-GinzburgWilson (LGW) model. For N = 3 this mapping allows us to conclude that the three-component ACP 2 model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP 2 and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N ≥ 4. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.

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“…Algebraically decaying correlations and frustration effects typically render two dimensional U(1) × Z 2 -symmetric models difficult to investigate numerically 18 . In this work we emply a non-equilibrium approach, namely that of short time critical dynamics (STCD).…”

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confidence: 99%

Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems

2013

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We discuss the phase diagram and phase transitions in U (1)×Z2 three-band superconductors with broken time reversal symmetry. We find that beyond mean field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken Z2 time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different Z2 states is low and thus fluctuations restore broken time reversal symmetry in the superconducting state at low temperatures.In recent years, the discovery of superconductors such as the Iron Pnictides 1 , has generated much interest for multiband superconducting systems. From a theoretical viewpoint, one of the main reasons for the strong interest is that in contrast to previously known two-band materials, iron-based superconductors may exhibit dramatically different physics due to the possibility of frustrated inter-band Josephson couplings originating with more than two bands crossing the Fermi-surface 2-5 . In two-band superconductors the Josephson coupling locks the phase differences between the bands to 0 or π. By contrast, if one has three bands and the frustration of interband coupling is sufficiently strong, the ground state interband phase difference can be different from 0 or π. This leads to a superconducting state which breaks time reversal symmetry (BTRS) 2,3 . From a symmetry viewpoint such a ground state breaks U(1) × Z 2 4 . Recently, such a scenario has received solid theoretical support 5 in connection with hole-doped Ba 1 − x K x Fe 2 As 2 . The possibility of this new physics arising also in other classes of materials is currently under investigation 6 . For other scenarios of time reversal symmetry breakdown in ironbased superconductors discussed in the literature, see 7,8 .Three band superconductors with frustrated interband Josephson couplings feature several properties that are radically different from their two-band counterparts. These include (I) the appearance of a massless so-called Leggett mode at the Z 2 phase transition 9 ; (II) the existence of new mixed phase-density collective modes in the state with broken time-reversal symmetry (BTRS) 4,5,10 in contrast to the "phase-only" Leggett collective mode in two-band materials 11 ; and (III) the existence of (meta-)stable excitations characterized by CP 2 topological invariants 12,13 . So far the phase diagram of frustrated three-band superconductors has been investigated only at the meanfield level 3,5 . However, the iron-based materials feature relatively high T c , as well as being far from the type-I regime. Hence, one may expect fluctuations to be of importance.In this paper, we study the phase diagram of a threeband superconductor in two spatial dimensions in the London limit, beyond mean-field approximation. The results should apply to relatively thin films of ironbased superconducto...

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Multicritical behaviour in the fully frustratedXYmodel and related systems

Cited by 100 publications

References 121 publications

First-order transition induced by topological defects in theO(3)principal chiral model

First-order transition induced by topological defects in theO(3)principal chiral model

Three-dimensional antiferromagneticCPN−1models

Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems

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