Finite-size scaling study of the three-dimensional classical XY model

Superconductor-insulator transition in space charge doped one unit cell Bi2.1Sr1.9CaCu2O8+x

The superconductor-insulator transition in two dimensions is a prototype continuous quantum phase transition at absolute zero, driven by a parameter other than temperature. Here we reveal this transition in one unit-cell Bi_2.1Sr_1.9CaCu₂O_8+x by space charge doping, a field effect electrostatic doping technique. We determine the related critical parameters and develop a reliable way to estimate doping in the nonsuperconducting region, a crucial and central problem in these materials. Finite-size scaling analysis yields a critical doping of 0.057 holes/Cu, a critical resistance of ~6.85 kΩ and a scaling exponent product νz ~ 1.57. These results, together with earlier work in other materials, provide a coherent picture of the superconductor-insulator transition and its bosonic nature in the underdoped regime of emerging superconductivity in high critical temperature superconductors.

Previous work on critical scaling at the superconductor-to-insulator transition has shown variations across different materials. Here, the authors use a space charge doping technique to tune the transition in a single layer cuprate sample and present evidence of the universal scaling behaviour.

Quantum Criticality at the Superconductor-Insulator Transition Probed by the Nernst Effect

The superconductor-insulator transition (SIT) is an excellent example of a quantum phase transition at zero temperature, dominated by quantum fluctuations. These are expected to be very prominent close to the quantum critical point. So far, most of the experimental studies of the SIT have concentrated on transport properties and tunneling experiments that provide indirect information on criticality close to the transition. Here we present an experiment uniquely designed to study the evolution of quantum fluctuations through the quantum critical point. We utilize the Nernst effect, which has been shown to be effective in probing superconducting fluctuation. We measure the Nernst coefficient in amorphous indium oxide films tuned through the SIT and find a large signal on both the superconducting and the insulating sides, which peaks close to the critical point. The transverse Peltier coefficient α_{xy}, which is the thermodynamic quantity extracted from these measurements, follows quantum critical scaling with critical exponents ν∼0.7 and z∼1. These exponents are consistent with a clean X-Y model in 2+1 dimensions.

Monte Carlo simulations of the XY vectorial Blume-Emery-Griffiths model in multilayer films for ^{3}He-^{4}He mixtures

The XY vectorial generalization of the Blume-Emery-Griffiths (XY-VBEG) model, which is suitable to be applied to the study of ^{3}He-^{4}He mixtures, is treated on thin films structure and its thermodynamical properties are analyzed as a function of the film thickness. We employ extensive and up-to-date Monte Carlo simulations consisting of hybrid algorithms combining lattice-gas moves, Metropolis, Wolff, and super-relaxation procedures to overcome the critical slowing down and correlations among different spin configurations of the system. We also make use of single histogram techniques to get the behavior of the thermodynamical quantities close to the corresponding transition temperatures. Thin films of the XY-VBEG model present a quite rich phase diagram with Berezinskii-Kosterlitz-Thouless (BKT) transitions, BKT endpoints, and isolated critical points. As one varies the impurity concentrations along the layers, and in the limit of infinite film thickness, there is a coalescence of the BKT transition endpoint and the isolated critical point into a single, unique tricritical point. In addition, when mimicking the behavior of thin films of ^{3}He-^{4}He mixtures, one obtains that the concentration of ^{3}He atoms decreases from the outer layers to the inner layers of the film, meaning that the superfluid particles tend to locate in the bulk of the system.

Competing nematic interactions in a generalized XY model in two and three dimensions

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of 2π/q between neighboring spins. We focus here on the q=8 case (while presenting new results for other values of q as well) whose phase diagram is much richer than the well-known q=2 case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in q=2, but also infinite-order transitions involving intermediate, competition-driven phases absent for q=2 and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a sufficient condition for it to be of BKT type.

Classical lattice spin models involving singular interactions isotropic in spin space

We address here a few classical lattice spin models, involving n-component unit vectors (n=2,3), associated with a D-dimensional lattice Z(D),D=1,2, and interacting via a pair potential restricted to nearest neighbors and being isotropic in spin space, i.e., defined by a function of the scalar product between the interacting spins. When the potential involves a continuous function of the scalar product, the Mermin-Wagner theorem and its generalizations exclude orientational order at all finite temperatures in the thermodynamic limit, and exclude phase transitions at finite temperatures when D=1; on the other hand, we have considered here some comparatively simple functions of the scalar product which are bounded from below, diverge to +∞ for certain mutual orientations, and are continuous almost everywhere with integrable singularities. Exact solutions are presented for D=1, showing an absence of phase transitions and an absence of orientational order at all finite temperatures in the thermodynamic limit; for D=2, and in the absence of more stringent mathematical results, extensive simulations carried out on some of them point to the absence of orientational order at all finite temperatures and suggest the existence of a Berezinskiĭ-Kosterlitz-Thouless transition.

Winding number excitation detects phase transition in one-dimensional XY model with variable interaction range

We numerically study the critical behavior of the one-dimensional XY model of the size N with variable interaction range L. As expected, the standard local order parameter of the magnetization is shown to well detect the mean-field-type transition which occurs at any nonzero value of L/N. The system is particularly interesting since the underlying one-dimensional structure allows us to study the topological excitation of the winding number across the whole system even though the system shares the mean-field transition with the globally coupled system. We propose a nonlocal order parameter based on the width of the winding number distribution which exhibits a clear signature of the transition nature of the system.

Traveling wave in a three-dimensional array of conformist and contrarian oscillators

We consider a system of conformist and contrarian oscillators coupled locally in a three-dimensional cubic lattice and explore collective behavior of the system. The conformist oscillators attractively interact with the neighbor oscillators and therefore tend to be aligned with the neighbors' phase. The contrarian oscillators interact repulsively with the neighbors and therefore tend to be out of phase with them. In this paper, we investigate whether many peculiar dynamics that have been observed in the mean-field system with global coupling can emerge even with local coupling. In particular, we pay attention to the possibility that a traveling wave may arise. We find that the traveling wave occurs due to coupling asymmetry and not by global coupling; this observation confirms that the global coupling is not essential to the occurrence of a traveling wave in the system. The traveling wave can be a mechanism for the coherent rhythm generation of the circadian clock or of hormone secretion in biological systems under local coupling.

Nematic order by thermal disorder in a three-dimensional lattice spin model with dipolarlike interactions

At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example, nearest-neighbor interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second-rank) order, in addition to the primary first-rank one; on the other hand, in the literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with finite-size scaling analysis, have been used for characterizing its critical behavior; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder.

Multiple quantum criticality in a two-dimensional superconductor

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Vortex glass transition in a frustrated 3D XY model with disorder

The anisotropic frustrated three-dimensional (3D) XY model with disorder in the coupling constants is simulated as a model of a point disordered superconductor in an applied magnetic field. A finite size scaling analysis of the helicity modulus gives strong evidence for a finite temperature transition with isotropic scaling and the correlation length exponent nu=1.5+/-0.3, consistent with 3D gauge glass universality.