Mode-coupling theory predictions for a limited valency attractive square-well model

Recently we have studied, using numerical simulations, a limited valency model, i.e. an attractive square well model with a constraint on the maximum number of bonded neighbors. Studying a large region of temperatures $T$ and packing fractions $\phi$, we have estimated the location of the liquid-gas phase separation spinodal and the loci of dynamic arrest, where the system is trapped in a disordered non-ergodic state. Two distinct arrest lines for the system are present in the system: a {\it (repulsive) glass} line at high packing fraction, and a {\it gel} line at low $\phi$ and $T$. The former is essentially vertical ($\phi$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(\phi-T)$ plane. We here complement the molecular dynamics results with mode coupling theory calculations, using the numerical structure factors as input. We find that the theory predicts a repulsive glass line -- in satisfactory agreement with the simulation results -- and an attractive glass line which appears to be unrelated to the gel line.Comment: 12 pages, 6 figures. To appear in J. Phys. Condens. Matter, special issue: "Topics in Application of Scattering Methods for Investigation of Structure and Dynamics of Soft Condensed Matter", Fiesole, November 200

Percolation transition and the onset of non exponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in 2 and 3 dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ``large scale'' effects of frustration, present below the percolation threshold. Moreover these results are consistent with the picture suggested by Campbell et al. in space of configurations.Comment: 8 pages, 11 figures, revised versio

Percolation transition of hydration water at hydrophilic surfaces

An analysis of water clustering is used to study the quasi-2D percolation transition of water adsorbed at planar hydrophilic surfaces. Above the critical temperature of the layering transition (quasi-2D liquid-vapor phase transition of adsorbed molecules) a percolation transition occurs at some threshold surface coverage, which increases with increasing temperature. The location of the percolation line is consistent with the existence of a percolation transition at the critical point. The percolation threshold at a planar surface is weakly sensitive to the size of the system when its lateral dimension increases from 80 to 150 A. The size distribution of the largest water cluster shows a specific two-peaks structure in a wide range of surface coverage : the lower- and higher-size peaks represent contributions from non-spanning and spanning clusters, respectively. The ratio of the average sizes of spanning and non-spanning largest clusters is about 1.8 for all studied planes. The two-peak structure becomes more pronounced with decreasing size of the planar surface and strongly enhances at spherical surfaces.Comment: 17 pages, 11 figure

Invaded cluster algorithm for a tricritical point in a diluted Potts model

The invaded cluster approach is extended to 2D Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the two-dimensional parameter space spanned by temperature and the chemical potential of vacancies. The tricritical point is identified as a simultaneous onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of "geometrical disorder cluster". The location of the tricritical point and the concentration of vacancies for q = 1, 2, 3 are found to be in good agreement with the best known results. Scaling properties of the percolating scaling cluster and related critical exponents are also presented.Comment: 8 pages, 5 figure

Theory of continuum percolation I. General formalism

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting $s$-state spins which are free to move in the continuum. In the $s \to 1$ limit, the Potts magnetization, susceptibility and correlation functions are directly related to the percolation probability, the mean cluster size and the pair-connectedness, respectively. Through the Hamiltonian formulation of the Potts fluid, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem.Comment: 26 pages, Late

Non exponential relaxation in fully frustrated models

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.Comment: 7 pages, RevTeX, 11 figs, to appear on Physical Review

Phase transitions in the Potts spin glass model

We have studied the Potts spin glass with 2-state Ising spins and s-state Potts variables using a cluster Monte Carlo dynamics. The model recovers the +- J Ising spin glass (SG) for s=1 and exhibits for all s a SG transition at T_{SG}(s) and a percolation transition at higher temperature T_p(s). We have shown that for all values of $s\neq 1$ at T_p(s) there is a thermodynamical transition in the universality class of a ferromagnetic s-state Potts model. The efficiency of the cluster dynamics is compared with that of standard spin flip dynamics.Comment: 8 pages, Latex, with 8 EPS fig

An Experimental and Semi-Empirical Method to Determine the Pauli-Limiting Field in Quasi 2D Superconductors as applied to κ\kappa-(BEDT-TTF)2_2Cu(NCS)2_2: Strong Evidence of a FFLO State

We present upper critical field data for $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ with the magnetic field close to parallel and parallel to the conducting layers. We show that we can eliminate the effect of vortex dynamics in these layered materials if the layers are oriented within 0.3 degrees of parallel to the applied magnetic field. Eliminating vortex effects leaves one remaining feature in the data that corresponds to the Pauli paramagnetic limit ($H_p$). We propose a semi-empirical method to calculate the $H_p$ in quasi 2D superconductors. This method takes into account the energy gap of each of the quasi 2D superconductors, which is calculated from specific heat data, and the influence of many body effects. The calculated Pauli paramagnetic limits are then compared to critical field data for the title compound and other organic conductors. Many of the examined quasi 2D superconductors, including the above organic superconductors and CeCoIn$_5$, exhibit upper critical fields that exceed their calculated $H_p$ suggesting unconventional superconductivity. We show that the high field low temperature state in $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ is consistent with the Fulde Ferrell Larkin Ovchinnikov state.Comment: 8 pages, 9 figures, 10 years of dat

Upper critical field study in the organic superconductor β′′\beta''-(ET)2_{2}SF5_{5}CH2_{2}CF2_{2}SO3_{3} : Possibility of Fulde-Ferrell-Larkin-Ovchinnikov state

We report upper critical field measurements in the metal-free-all-organic superconductor $\beta''$-(ET)$_{2}$SF$_{5}$CH$_{2}$CF$_{2}$SO$_{3}$ obtained from measuring the in-plane penetration depth using the tunnel diode oscillator technique. For magnetic field applied parallel to the conducting planes the low temperature upper critical fields are found to exceed the Pauli limiting field calculated by using a semi-empirical method. Furthermore, we found a signature that could be the phase transition between the superconducting vortex state and the Fulde-Ferrell-Larkin-Ovchinnikov state in the form of a kink just below the upper critical field and only at temperatures below 1.23 K.Comment: 4 pages, 6 figure

Damage spreading in random field systems

We investigate how a quenched random field influences the damage spreading transition in kinetic Ising models. To this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random field systems. This theory is applied to the Glauber Ising model with a bimodal random field distribution. We find that the random field influences the spreading transition by two different mechanisms with opposite effects. First, the random field favors the same particular direction of the spin variable at each site in both systems which reduces the damage. Second, the random field suppresses the magnetization which, in turn, tends to increase the damage. The competition between these two effects leads to a rich behavior.Comment: 4 pages RevTeX, 3 eps figure