xy model magnetization
November 13th, 2020

To be published in Physical Review B1 01Jun98. Comment: updated figures and texts. These characteristics match closely those obtained for nonmagnetic, twinned YBa2Cu3O7.00. The experimental situation is discussed. 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. ) – T We discuss the observable signature of this crossover in decoration experiments and in neutron diffraction experiments on flux lattices. γ2 is found to have two characteristic contributions. So far, the results from PCA and variational autoencoders both suffer from learning the energy or magnetization instead of vorticity [5-8]. This contribution persists at all temperatures near or below Tc, and dominates over the first contribution above a site dilution of about 10%. The simulation gives estimates on the jumps of entropy and magnetic induction on the melting in good agreement with the experimental observation on a YBa2Cu3O7-δ single crystal. However at low temperatures for a finite system, the mean … The possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation. Previously I de ned the expectation value of the spin to be the magnetization M, with no brackets. Up to higher-order corrections We report adiabatic specific heat measurements for a high-purity YBa2Cu3Ox twinned single crystal. ��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� The Liouville equation for the XY model is solved exactly, and the magnetization is computed explicitly. shows the corresponding behavior in 3D, at f = 1/24 and 1/6. We show analytically that the intralayer interaction energy can be evaluated using the Ewald summation technique. The fractional fluxons are basically walls between different domains of the ground state of the underlying 1∕q lattice. c Although the agreement is not as good as with the YBa2Cu3O7-δ sample, the simulation results are comparable with the experimental observation on a Bi2Sr2CaCu2O8 sample. The order of the transition on the melting line of the vortex system Bm\(T\) is investigated for three oxygen concentrations. This is perhaps not surprising since, while in the thermodynamic limit the 2D XY model has no magnetization, a finite-size system has a very large magnetization in the low-temperature region. It is argued that the helicity modulus of the frustrated 2D XY model vanishes for any finite temperature in the limit of weak frustration $f$. m() L We have studied the statics and dynamics of flux lines in a model for YBa2Cu3O7-δ, using both Monte Carlo simulations and Langevin dynamics. The phase-ordering transition temperature Tc is determined as the temperature at which ns goes to zero. At the upper transition, there is a sharp increase in magnetization, in qualitative agreement with recent local Hall probe experiments. The calculated melting curve and many dynamical features agree well with experiment. One piece of notation needs some explanation. A jump in the helicity modulus along the c axis is observed at the melting point from zero to 16π3λab2(Tm)Υc(Tm)Γ2/(dφ02)≃0.6 with Γ the anisotropy constant in the present model. We study via Monte Carlo simulation the effective superfluid density ns and the real part of the integrated fluctuation conductivity, γ2, of a model granular superconductor in which the individual superconducting grains are coupled via Josephson tunneling. The entropy jump reaches a maximum value of 0.45kB/vortex/layer at a field ∼10Bcr and decreases with decreasing field due to an increase in the transition temperature. To realize the continous spin, all spins are represented as (cosx, sinx) The temperature dependence of energy (XY Model) The temperature dependence of magnetization (XY Model) Therefore, the system is superconducting only below Tm and along the c axis. The starting point is the Ginzburg-Landau theory in presence of an external magnetic field H. A set of fictitious vortex variables and a singular gauge transformation are used to rewrite a finite H Ginzburg-Landau functional in terms of a complex scalar field of zero average vorticity. A possibility of a novel phase transition involving zero vorticity degrees of freedom and formation of a uniform condensate is suggested. 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. �-�l���_+��?�� �U�|o�6��8��`��j, make up protons, neutrons, etc. Qualitative arguments are given suggesting the existence for weak disorder in $d=3$ of a `` Bragg glass '' phase without free dislocations and with algebraically divergent Bragg peaks. The vectors correspond to the directions of spins (originally quantum mechanical) in a material A model of the effective interaction between the magnetic flux-lines in a layered superconductor is derived from the Lawrence–Doniach 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. Phase coherence parallel to the field persists until a sharp crossover, conceivably a phase transition, near $T_{\ell} > T_m$ which develops at the same temperature as an infinite vortex tangle. Comment: Updated references. For the statics we use a frustrated 3D XY model on a stacked triangular lattice. It is characterized by the proliferation of vortex-antivortex pairs (in 2D) or vortex loops (in 3D). m(L When one additional fluxon is added to the ladder, it breaks up into q fractional fluxons, each carrying 1∕q units of vorticity. Using an improved estimator in the loop-cluster algorithm, we investigate the constraint effective potential of the magnetization in the spin \frac {1}{2} quantum XY model. We have numerically studied the statics and dynamics of a model three-dimensional vortex lattice at low magnetic fields. We apply our results to determine the extent of longitudinal correlations in YBCO just above melting. Therefore, the origin of this melting transition is the entanglement of flux lines. 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. The region is characterized by several distinct features: (i) the melting of the lattice occurs when the Josephson energy is suppressed to 64% of its bare value; (ii) the latent heat at the transition does not change much with the anisotropy parameter; (iii) the jump of the Josephson energy at the transition is equal to the jump of the in-plane energy. For a clean system, both approaches yield the same melting curve, which is found to be weakly first order with a heat of fusion of about 0.02kBTm per vortex pancake at a field of 50 kG. To illustrate the usefulness of the simulation technique, the isothermal shear modulus c66 of flux-line lattices with various values of the interlayer coupling strength was obtained with a Langevin dynamics simulation. 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 calculated melting curve and many dynamical features agree well with experiment. We find a very broad crossover region between quasi-two-dimensional and line-like melting regimes ranging from ∼Bcr to ∼10Bcr. A model of the effective interaction between the magnetic flux-lines in a layered superconductor is derived from the Lawrence-Doniach model.

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