Critical behavior of thermal relaxation near a breakdown point

At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of a sufficiently large value is passed through the sample. If the current is less than a certain breakdown current (I(b)) the resistance eventually reaches a steady value with a characteristic relaxation time tau(h). The latter diverges with current I as tau(h) approximately (1-I(2)/I(2)(b))(-z). The value of the exponent z displays large fluctuations leading to unusual scaling of the relaxation time. It is shown that the results lead to important conclusions about the nature of breakdown phenomena.     

Critical behavior and coexistence near a superconducting-ferromagnetic multicritical point

It is shown that in the vicinity of the multicritical transition point of a ferromagnetic cuperconductor a) critical fluctuations of the superconducting order parameter should become observable in 3 dimensions, b) for planar magnetic ordering magnetism and superconductivity should coexist.     

Large Wilson loop averages from the Schwinger-Dyson equation

Using Schwinger-Dyson equations for the large Wilson loop in abelian lattice gauge theories, we evaluate the vacuum expectation values of the Wilson loop of sizes 1 × 2, 2 × 2, 2 × 3, and so on, from which the string tension is extracted.     

Confinement,the Wilson loop and the gluon propagator

We show that if the gluon propagator has a highly singular infrared behavior (such as $\text{1}\text{q}{}^4$) in any one gauge then the Wilson loop must fall exponentially to zero with an area law, indicative of confinement. The proof of this claim follows from an inequality derived via a mean value theorem.     

Glueball spectrum and Pomeron in the Wilson loop approach

Using a nonperturbative method based on the asymptotic behavior of Wilson loops, we calculate the masses of glueballs and the corresponding Regge trajectories. The only input is the string tension fixed by the meson Regge slope, while perturbative contributions to spin splittings are defined by standard α_s values. The masses of the lowest glueball states are in a perfect agreement with lattice results. The leading glueball trajectory, which is associated with the Pomeron is discussed in detail, and its mixing with f and f′ trajectories is taken into account.     

Weak coupling perturbative calculations of the Wilson loop for the standard action

Wilson loops of size m × n with m, n≤6 are evaluated to second order in weak coupling perturbation theory. The results are compared with earlier estimates by Hattori and Kawai.     

Surface representations of Wilson loop expectations in lattice gauge theory

Expectations of Wilson loops in lattice gauge theory with gauge group $\text{G}\text{=}\text{Z}{}_2$, U(1) or SU(2) are expressed as weighted sums over surfaces with boundary equal to the loops labelling the observables. For $\text{G}\text{=}\text{Z}{}_2$ and U(1), the weighted are all positive. For G = SU(2), the weights can have either sign depending on the Euler characteristic of the surface. Our surface (or flux sheet-) representations are partial resummations of the strong coupling expansion and provide some qualitative understanding of confinement. The significance of flux sheets with nontrivial topology for permanent confinement in the SU(2)-theory is elucidated.     

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory are carried out numerically up to order g⁴. Comparison of the results with those of the Monte Carlo calculations shows that there exists a non-perturbative contribution of an essential singularity type which may be identified as the string tension.     

Critical point in complex plasmas

The occurrence of liquid-vapor phase transition and the possible existence of a critical point in complex plasmas--systems that consist of charged micrograins in a neutralizing plasma background--is investigated theoretically. An analysis based on the consideration of the intergrain interaction potential suggests that under certain conditions systems near and at the critical point should be observable. Measurements under microgravity conditions would appear to be required. The analysis aims at determining the plasma parameter regime most suitable for planned experimental investigations.     

Critical behavior of the Chayes-Machta-Swendsen-Wang dynamics

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z >or= alpha/nu is close to but probably not sharp in d = 2 and is far from sharp in d = 3, for all q. The conjecture z >or= beta/nu is false (for some values of q) in both d = 2 and d = 3.