The model has an interesting phase diagram describing quantumphase transitions (QPTs) belonging to two diﬀerent universality classes. The entropy jump is 0.5±0.1 kB/vortex/layer. It is revealed that three transition lines of the vortex-lattice melting line H m(T), the vortex-glass transition line Hg(T), and the field-driven disordering transition line H*(T) terminate at the critical point and divide the vortex-matter phase into three different phases: the vortex liquid, the Bragg glass, and the vortex glass. So far, the results from PCA and variational autoencoders both suffer from learning the energy or magnetization instead of vorticity [5-8]. m c c It follows that the zero-temperature penetration depth λp(0) of the granular superconductor varies as the square root of the normal-state resistivity. When one additional fluxon is added to the ladder, it breaks up into q fractional fluxons, each carrying 1∕q units of vorticity. The melting of flux line lattices is studied using Langevin dynamics simulation of the model with various values of interlayer coupling strength and pinning intensities. Constraint eﬀective potential of the magnetization in the quantum XY model The low-energy eﬀective ﬁeld theory is formulated in terms of the magnetization order parameter ﬁeld e(x)=(e1(x),e2(x)) ∈ S1,e(x)2 =1, (2.5) where x =(x1,x2,t) is a point in Euclidean space–time. For a two dimensional lattice G of side length N, the spin ~ may be given as a complex number of unit length where ˙ ~x= exp(i ~x) = cos( ~x) + isin( ~x) (1) The expectation value of an observable Ois then = 1 Z Z The lines are assumed to be flexible but unbroken in both the solid and liquid states. Data for less pure crystals are included for comparison purposes. Once again n/n 0 ∼ 1 below the zero field 3D XY transition at T XY , increasing markedly near T /J ∼ 2.0 for f = 1/24 and near 1.15J for f = 1/6. Even without pins, the model gives subdiffusive motion of individual pancakes in the dense liquid phase, with mean-square displacement proportional to t1/2 rather than to t as in ordinary diffusion. We have studied the statics and dynamics of flux lines in a model for YBa2Cu3O7-δ, using both Monte Carlo simulations and Langevin dynamics. Previously I de ned the expectation value of the spin to be the magnetization M, with no brackets. Applications to $d=2+0$ systems and experiments on magnetic bubbles are discussed. One piece of notation needs some explanation. These characteristics match closely those obtained for nonmagnetic, twinned YBa2Cu3O7.00. For f = 1/6, this increases occurs over a temperature range △T < 0.05J, just at the first order phase transition where both lattice order and phase coherence parallel to the field are destroyed (T m ∼ T ℓ for f = 1/6). The critical properties of the xy model with nearest-neighbour interactions on a two-dimensional square lattice are studied by a renormalization group technique. m() L 2 XY model In the classical xy-model, the variables are two-dimensional unit vectors ~s i on each lattice site, equivalent to an angle θ. , d = 1. We model the dynamics as a coupled network of overdamped resistively-shunted Josephson junctions with Langevin noise. /Length 4 0 R field of 50 kG. At the upper transition, there is a sharp increase in magnetization, in qualitative agreement with recent local Hall probe experiments. Just below melting, the defects show a clear magnetic-field-dependent two- to three-dimensional crossover from long disclination lines parallel to the c axis at low fields, to two-dimensional ‘‘pancake’’ disclinations at higher fields. ��v+�Ƀ���>�=� o�����3n�� qB�"��PV �v����k.E|'�"y����b�=��lDdh#���pG~f�tr�Lo#�V�G8c��a�hMH�V�.6@:k�3���Y�5;��q���O�n�2�I qL���t����JR�U܃��t� /7���UI� %PDF-1.2 The IV characteristics in the pinned lattice can be analyzed in terms of the motion of defects in the vortex lattice, using real-time Delaunay triangulation. The magnetization, energy, susceptibility, heat capacity and correlation length are derived and well consis-tent with Monte Carlo simulation results. is clarified by Monte Carlo simulations of the 3D frustrated XY model. The magnetization relaxation time in a clean sample slows dramatically as the temperature approaches the mean-field upper critical field line Hc2(T) from below. This type of phase transition cannot occur in a superconductor nor in a Heisenberg ferromagnet. The application of these ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid are discussed. We have numerically studied the statics and dynamics of a model three-dimensional vortex lattice at low magnetic fields. The correlation length is found to diverge faster than any power of the =7˓��Q.rc^Dˮ� -��+���+.��L�t��$�!D�ÀRP��>\|�����ҢI:�W����gF��#�2�R6�Pb��kf��Z���z��bp��|��T��� The calculated flux flow resistivity in various geometries near$T=T_{\ell}$closely resembles experiment. Comment: Updated references. Above an intergrain normal-state resistance R∼R0=ℏ/e2, Tc falls significantly below the single-grain transition temperature Tc0, in agreement with our previous Monte Carlo results, and ns deviates substantially from typical bulk behavior. In$d=3$we compute the crossover function between the three regimes. new movies available at http://www.physics.ohio-state.edu:80/~ryu/jj.html. Effects of the weak point disorder on the vortex-matter phase diagram are also studied by the irradiation of 2.5 MeV electrons. The model is important in itself since it serves as a prime example of an equilibrium phase transition with topological order [13,14]. x�uˎ�6�>��^V�^��^�%���$����A�[b�DˢG������K��v���bU�X�R���/]�U�-�zU��,�Usz���ݿ�K�UZnU������oM�G��d;���C�C�⟛�я� ���N���׿�V�*M�uN� Comment: updated figures and texts. Contrary to the predictions of mean-field theory, this phase transition in Bi2Sr2CaCu2O8 is found to be first-order. In the London regime the phase diagram of layered superconductors is shown to be universal if plotted in scaled temperature and field with the field scale being the two-dimensional (2D)-three-dimensional (3D) crossover field Bcr. The fields Bm and peak temperatures Tm obey the relation Bm[T]=139(1-Tm/Tc)1.33. The second derivative ({partial_derivative}{sup 2}{ital M}/{partial_derivative}{ital T}{sup 2}){sub {ital H}} is predicted to be negative throughout the vortex liquid state and positive in the solid state. The relative change in vortex density, δn/n 0 , is less than 7 % for f = 1/6. Rigorous analysis of the XY model shows the magnetization in the thermodynamic limit is zero, and that the square magnetization approximately follows ≈ − /, which vanishes in the thermodynamic limit. The temperature dependence of the magnetization (3D Ising model) XY model This model is an ideal system which consists of spins which can face in any directions. Just below melting, the defects show a clear magnetic-field-dependent two- to three-dimensional crossover from long disclination lines parallel to the c axis at low fields, to two-dimensional ‘‘pancake’’ disclinations at higher fields. The local density of field induced vortices increases sharply near $T_\ell$, corresponding to the experimentally observed magnetization jump. The pancake alignment above the transition increases with increasing of the Josephson coupling. The vortex liquid discontinuously expands on freezing. shows the corresponding behavior in 3D, at f = 1/24 and 1/6. , while no sharp change can be found in the number and size distribution of vortex loops around T Even without pins, the model gives subdiffusive motion of individual pancakes in the dense liquid phase, with mean-square displacement proportional to t1/2 rather than to t as in ordinary diffusion. Norges Tekniske H~gskole. Accepted for publication in Physical Review Letters. All figure content in this area was uploaded by David Stroud, All content in this area was uploaded by David Stroud on Jan 31, 2013. The fully anisotropic transverse-ﬁeld XY model in one dimension (1d) describes an interacting spin system for which many exact results on ground and excited state properties including spin correlations are known [1–3]. Similarly, for an n-component spin (n= 2 is usually called the XY model, n= 3 the Heisenberg), one would de ne f(M~). γ2 is found to have two characteristic contributions. The continuum limit of the transformed problem takes the form of an H = 0 Ginzburg-Landau functional for a charged field coupled to a fictitious gauge' potential which arises from long wavelength fluctuations in the background liquid of field-induced vorticity. We present the first non-mean-field calculation of the magnetization {ital M}({ital T}) of YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} both above and below the flux-lattice melting temperature {ital T}{sub {ital m}}({ital H}), in good agreement with experiment. The vectors correspond to the directions of spins (originally quantum mechanical) in a material One is due to thermodynamic fluctuations and appears near Tc in ordered and weakly diluted lattices of superconducting grains.

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