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Register a new userVortex-line percolation in the three-dimensional complex |psi|^4 model
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In discussing the phase transition of the three-dimensional complex |psi|^4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using high-precision Monte Carlo techniques we investigate if both of them exhibit the same critical behavior leading to the same critical exponents and hence to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different connectivity definitions for constructing the vortex-loop network lead to different results in the thermodynamic limit, and the percolation thresholds do not coincide with the thermodynamic phase transition point.
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We study the phase transition of the three-dimensional complex |psi|^4 theory by considering the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using high-precision Monte Carlo techniques we examine an alternative formulation of the geometrical excitations in relation to the global O(2)-symmetry breaking, and check if both of them exhibit the same critical behavior leading to the same critical exponents and therefore to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different definitions of constructing the vortex-loop network lead to different results in the thermodynamic limit, and the percolation thresholds do not coincide with the thermodynamic phase transition point.
We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II su- perconductors, magnetic materials and aspects of cosmology. We characterise the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully-packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls-off algebraically and we associate it to a geometric percolation transition that we characterise in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermo- dynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach towards a state that, within numerical accuracy, shares many features with the one at the percolation threshold, a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops, and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length-scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.
A percolation transition in the vortex state of a superconducting 2H-NbSe2 crystal is observed in the regime where vortices form a heterogeneous phase consisting of ordered and disordered domains. The transition is signaled by a sharp increase in critical current that occurs when the volume fraction of disordered domains, obtained from pulsed measurements of the current-voltage characteristics, reaches the value Pc= 0.26. Measurements on different vortex states show that while the temperature of the transition depends on history and measurement speed, the value of Pc and the critical exponent characterizing the approach to it, r =1.97 $pm$ 0.66, are universal.
We study the vortex-line lattice and liquid phases of a clean type-II superconductor by means of Monte Carlo simulations of the lattice London model. Motivated by a recent controversy regarding the presence, within this model, of a vortex-liquid regime with longitudinal superconducting coherence over long length scales, we directly compare two different ways to calculate the longitudinal coherence. For an isotropic superconductor, we interpret our results in terms of a temperature regime within the liquid phase in which longitudinal superconducting coherence extends over length scales larger than the system thickness studied. We note that this regime disappears in the moderately anisotropic case due to a proliferation, close to the flux-line lattice melting temperature, of vortex loops between the layers.
Interplay between antiferromagnetism and superconductivity is studied by using the 3-dimensional nearly half-filled Hubbard model with anisotropic transfer matrices $t_{rm z}$ and $t_{perp}$. The phase diagrams are calculated for varying values of the ratio $r_{rm z}=t_{rm z}/t_{perp}$ using the spin fluctuation theory within the fluctuation-exchange approximation. The antiferromagnetic phase around the half-filled electron density expands while the neighboring phase of the anisotropic $d_{x^{2}-y^{2}}$-wave superconductivity shrinks with increasing $r_{rm z}$. For small $r_{rm z}$ $T_{rm c}$ decreases slowly with increasing $r_{rm z}$. For moderate values of $r_{rm z}$ we find the second order transition, with lowering temperature, from the $d_{x^{2}-y^{2}}$-wave superconducting phase to a phase where incommensurate SDW coexists with $d_{x^{2}-y^{2}}$-wave superconductivity. Resonance peaks as were discussed previously for 2D superconductors are shown to survive in the $d_{x^{2}-y^{2}}$-wave superconducting phase of 3D systems. Soft components of the incommensurate SDW spin fluctuation mode grow as the coexistent phase is approached.
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