Observation of Ising-like critical fluctuations in frustrated Josephson junction arrays with modulated coupling energies

Affolter, J.; Tesei, M.; Pastoriza, H.; Leemann, Ch.; Martinoli, P.

doi:10.1016/s0921-4534(01)01266-7

Cited by 8 publications

(22 citation statements)

References 9 publications

(14 reference statements)

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“…The results agree quite precisely with the curve obtained in the standard XY model, see Appendix B. Thus, we conclude that the LT phase of the FFXY, φ 4 , and IsXY models is controlled by the same line of Gaussian fixed points that are relevant for the XY model.…”

Section: The Low-temperature Phasesupporting

confidence: 86%

“…19. At J = 0 we have an Ising transition at C = C Is = (3) 2627(3) 1.2029 (8) 121.1(6) 55.6(5) 37.55 (7) 31.3(2) 0.223 (2) 128 1.46782(3) 4865(7) 1.1957 (7) (3) 16247(50) 1.1773 (13) 328 (4) 131 (3) 52.5(3) 38.7 (7) 0.018(3) 360 1.46838 (3) 29466(133) 1.1724(15) 463(8) 177 (5) 52.7(4) 31.8 (9) 0.005 (4) region C < −C Is , bounding an antiferromagnetic phase. We have not investigated the behavior of the IsXY model along this antiferromagnetic transition line, although it is likely (but we have not numerically checked) that the second-order transition line turns into a first-order one as J increases, as it happens for the ferromagnetic case that we are going to discuss below.…”

Section: Phase Transitions In the Ising-xy Modelmentioning

confidence: 99%

“…It should describe the superconducting-to-normal transition at half a flux quantum per plaquette, see, e.g., Refs. [2,3,4] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…In the FFXY model and in the φ 4 and IsXY models in a large parameter region, the finite-size behavior at the chiral and spin transitions is model independent, apart from a length rescaling. In particular, the universal approach to the Ising regime at the chiral transition is nonmonotonic for most observables, and there is a wide region in which the finite-size behavior is controlled by an effective exponent ν eff ≈ 0.8.…”

Section: Introductionmentioning

confidence: 99%

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Multicritical behaviour in the fully frustratedXYmodel and related systems

Pelissetto²,

2005

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Abstract. We study the phase diagram and critical behavior of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on square lattices L × L, up to L = O(10 3 ). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range order.The FFXY model and the other models in a rather large parameter region show a crossover behavior at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behavior is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero-temperature transition. A possible candidate is the O(4) point that controls the low-temperature behavior of the 4-vector model.Multicritical behavior in the fully frustrated XY model and related systems 2

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Section: The Low-temperature Phasesupporting

confidence: 86%

Section: Phase Transitions In the Ising-xy Modelmentioning

confidence: 99%

“…It should describe the superconducting-to-normal transition at half a flux quantum per plaquette, see, e.g., Refs. [2,3,4] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multicritical behaviour in the fully frustratedXYmodel and related systems

Pelissetto²,

2005

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“…It combines vector spin-type symmetries with discrete chiral degrees of freedom, which result in the famous spin-chirality coupling at low temperatures [6]. However, experimental studies in solid-state systems are challenging in view of implementing and isolating an XY model Hamiltonian [7][8][9].Ultracold bosonic quantum gases in optical lattices, on the other hand, constitute a highly versatile system with an extraordinary degree of control [10,11]. In particular, the recent experimental realisations of artificial gauge potentials for bulk [12][13][14][15] and optical lattice systems [16][17][18][19] allow for the investigation of new physical regimes, not realisable in condensed matter systems.Here, we demonstrate the realisation of a system with combined U (1) and Z 2 symmetries using ultracold atoms submitted to artificial gauge fields.…”

mentioning

confidence: 99%

Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields

et al. 2013

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Emulation of gauge fields for ultracold atoms provides access to a class of exotic states arising in strong magnetic fields. Here we report on the experimental realisation of tunable staggered gauge fields in a periodically driven triangular lattice. For maximal staggered magnetic fluxes, the doubly degenerate superfluid ground state breaks both a discrete Z 2 (Ising) symmetry and a continuous U (1) symmetry. By measuring an Ising order parameter, we observe a thermally driven phase transition from an ordered antiferromagnetic to an unordered paramagnetic state and textbook-like magnetisation curves. Both the experimental and theoretical analysis of the coherence properties of the ultracold gas demonstrate the strong influence of the Z 2 symmetry onto the condensed phase.Phase transitions in systems with combined continuous and discrete symmetries are fundamentally different from their purely continuous and discrete counterparts. The interplay between different types of excitations in the various degrees of freedom can lead to a complex behaviour and coupling of the associated order parameters [1][2][3][4][5]. A paradigm example is the fully frustrated XY model on a triangular lattice. It combines vector spin-type symmetries with discrete chiral degrees of freedom, which result in the famous spin-chirality coupling at low temperatures [6]. However, experimental studies in solid-state systems are challenging in view of implementing and isolating an XY model Hamiltonian [7][8][9].Ultracold bosonic quantum gases in optical lattices, on the other hand, constitute a highly versatile system with an extraordinary degree of control [10,11]. In particular, the recent experimental realisations of artificial gauge potentials for bulk [12][13][14][15] and optical lattice systems [16][17][18][19] allow for the investigation of new physical regimes, not realisable in condensed matter systems.Here, we demonstrate the realisation of a system with combined U (1) and Z 2 symmetries using ultracold atoms submitted to artificial gauge fields. Our experimental setup consists of an ultracold gas of 87 Rb atoms held in a two-dimensional triangular lattice [20] (see Fig. 1a). At each lattice site j with particle number N j , the weakly interacting superfluid gas can be described by the local order parameter a j = N j e iϕj . As a central aspect, the local phases ϕ j are mapped onto classical XY spins s j = (cos ϕ j , sin ϕ j ), where the tunneling matrix elements between neighbouring lattice sites correspond to the spinspin coupling parameters. Such classical spins possess a continuous degree of freedom. In presence of a long-range order, analogous to the onset of Bose-Einstein condensation (BEC), the order parameter assumes an arbitrary, but fixed phase, thus breaking the continuous U (1) symmetry [21].Beyond that, we experimentally engineer strong staggered gauge fields, which generate an additional discrete Z 2 symmetry in our system. The resulting magnetic flux induces cyclotron-like mass currents around each plaquette. The two poss...

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Kosterlitz–Thouless physics: a review of key issues

2016

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This article reviews, from a very personal point of view, the origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the experimental verifications of the theory and some numerical simulations. Finally applications to superconducting arrays of Josephson junctions and to recent cold atom experiments are described.

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Observation of Ising-like critical fluctuations in frustrated Josephson junction arrays with modulated coupling energies

Cited by 8 publications

References 9 publications

Multicritical behaviour in the fully frustratedXYmodel and related systems

Multicritical behaviour in the fully frustratedXYmodel and related systems

Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields

Kosterlitz–Thouless physics: a review of key issues

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