The phase transition in a model for vortex lines in high temperature superconductors with columnar defects, i.e., linearly correlated quenched random disorder, is studied with finite size scaling and Monte Carlo simulations. Previous studies of critical properties have mainly focused on the limit of strongly screened vortex line interactions. Here the opposite limit of weak screening is considered. The simulation results provide evidence for a distinct universality class, with values of the critical exponents that differ from the case of strong screening of the vortex interaction. In particular, scaling is anisotropic and characterized by a nontrivial value of the anisotropy exponent $\ensuremath{\zeta}={\ensuremath{\nu}}_{\ensuremath{\Vert}}/{\ensuremath{\nu}}_{\ensuremath{\perp}}.$ The exponents we find, $\ensuremath{\zeta}=1.25\ifmmode\pm\else\textpm\fi{}0.1,{\ensuremath{\nu}}_{\ensuremath{\perp}}=1.0\ifmmode\pm\else\textpm\fi{}0.1,z=1.95\ifmmode\pm\else\textpm\fi{}0.1,$ are similar to certain experimental results for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}.$
The phase transition in a model for vortex lines in high temperature superconductors with columnar defects, i.e., linearly correlated quenched random disorder, is studied with finite size scaling and Monte Carlo simulations. Previous studies of critical properties have mainly focused on the limit of strongly screened vortex line interactions. Here the opposite limit of weak screening is considered. The simulation results provide evidence for a distinct universality class, with values of the critical exponents that differ from the case of strong screening of the vortex interaction. In particular, scaling is anisotropic and characterized by a nontrivial value of the anisotropy exponent \ensuremathζ=\ensuremathν\ensuremath∥/\ensuremathν\ensuremath⊥. The exponents we find, \ensuremathζ=1.25\ifmmode±\else\textpm\fi0.1,\ensuremathν\ensuremath⊥=1.0\ifmmode±\else\textpm\fi0.1,z=1.95\ifmmode±\else\textpm\fi0.1, are similar to certain experimental results for YBa2Cu3O7.
We investigate the effect of random columnar disorder on the superconducting phase transition of a type-II superconductor in zero applied magnetic field using numerical simulations of three dimensional XY and vortex loop models. We consider both an unscreened model, in which the bare magnetic penetration length is approximated as infinite, and a strongly screened model, in which the magnetic penetration length is of order the vortex core radius. We consider both equilibrium and dynamic critical exponents. We show that, as in the disorder free case, the equilibrium transitions of the unscreened and strongly screened models lie in the same universality class, however scaling is now anisotropic. We find for the correlation length exponent $\ensuremath{\nu}=1.2\ifmmode\pm\else\textpm\fi{}0.1$, and for the anisotropy exponent $\ensuremath{\zeta}=1.3\ifmmode\pm\else\textpm\fi{}0.1$. We find different dynamic critical exponents for the unscreened and strongly screened models.
Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences.
Phase transitions in a number of models related to hightemperature superconductors are investigated, using scalingmethods and Monte Carlo simulations. This thesis considers twomain topics. The first topic is phase transitions, phase diagrams, andvortex motion in high temperature superconductors at finitetemperature, subject to magnetic fields and disorder. We studya vortex glass model at finite temperature, with stronguncorrelated vortex pinning and a magnetic field. We find thatthe vortex glass exists at finite temperature and calculate thecritical exponents of the transition. We also investigate hightemperature superconductors with columnar disorder in zero andapplied magnetic fields. Some of these studies are alsorelevant for the superfluid to Mott insulator transition ofbosons in two dimensions. We find that the unscreened Boseglass transition belongs to a new universality class. Wecalculate the critical exponents of the superconductingtransition with columnar defects in zero applied magneticfield. The transverse Meissner transition is studied, and wefind an exotic universality class with a correlation volumethat is infinitely anisotropic in all directions. The second topic is confinement-deconfinement transitions incompact Abelian Higgs models. We develop a new order parameter,related to a large Wilson loop for fractionalized charges, anduse it to study the concept of topological order. Thesetransitions may be relevant for strongly correlated electronsin two dimensions.
Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences.
We present a finite temperature Monte Carlo study of the XY model in the vortex representation and study its dynamical critical behavior in two limits. The first neglects magnetic-field fluctuations, corresponding to the absence of screening, which should be a good approximation in high-Tc superconductors $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ except extremely close to the critical point. Here, from finite-size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be $z\ensuremath{\approx}1.5$. The second limit includes magnetic-field fluctuations in the strong screening limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}0)$ corresponding to the true asymptotic inverted XY critical regime, where we find the unexpectedly large value $z\ensuremath{\approx}2.7.$ We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin-wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.
We study vortex lines in high-temperature superconductors with columnar defects produced by heavy-ion irradiation. We reconsider scaling theory for the Bose-glass transition with tilted magnetic fields, and propose, e.g. , a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a screened interaction. Critical exponents are determined from scaling analysis of Monte Carlo data for current-voltage characteristics and other quantities. The dynamic critical exponent is found to be z = 4.6 ± 0.3.