The analysis of ac magnetic susceptibility data has shown that mechanically alloyed Fe30Ag40W30 , a highly heterogeneous nanogranular system, exhibits critical dynamics in its transition to a low-temperature spin-glasslike phase, as proved by the power-law divergence of the relaxation time at Tg519.7 K, and by the dynamic scaling behavior of the out-of-phase component of the susceptibility. Bot...

In this paper we study the on and oo-equilibrium properties of the four dimensional Gaussian spin glass. In the static case we determine with more precision that in previous simulations both the critical temperature as well as the critical exponent. In the oo-equilibrium case we settle the general form of the autocorrelation function , and show that is possible to obtain dynamically, for the rs...

We study positive supersolutions to an elliptic equation (∗) −∆u = c|x|u, p, s ∈ R, in cone–like domains in R (N ≥ 2). We prove that in the sublinear case p < 1 there exists a critical exponent p∗ < 1 such that equation (∗) has a positive supersolution if and only if −∞ < p < p∗. The value of p∗ is determined explicitly by s and the geometry of the cone.

Abstract. A review of recent progress in numerical studies of the Anderson transition in three dimensional systems is presented. From high precision calculations the critical exponent ν for the divergence of the localization length is estimated to be ν = 1.57 ± 0.02 for the orthogonal universality class, which is clearly distinguished from ν = 1.43 ± 0.03 for the unitary universality class. The...

Using a variant of the Sobolev Embedding Theorem, we prove an uncertainty principle related to Gabor systems that generalizes the Balian-Low Theorem. Namely, if f ∈ H(R) and f̂ ∈ H /2(R) with 1 < p < ∞, 1 p + 1 p′ = 1, then the Gabor system G(f, 1, 1) is not a frame for L(R). In the p = 1 case, we obtain a generalization of the result in [BCPS].

We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, wh...

A new method based on the R-operation of the renormalization theory is proposed for the numerical calculation of the renormalization constants in the theory of critical behaviour. The problem of finding residues of the poles of the Green’s functions at ε = 0, where ε = 4−d, is reduced to the evaluation of multiple UV-finite integrals, which can be performed by means of standard integration prog...

In class, we approached critical phenomena from the view point of correlation functions and discussed renormalization group methods for obtaining values of critical exponents. Here I discuss a parallel idea that studies critical phenomena from properties of random curves which form the domain walls of the critical system. It will be shown that such random curves obey a stochastic differential e...

We study a variable exponent model for image restoration in the case that the exponent attains the critical value one. We prove existence and Γ-convergence. The results answer an open question by Li, Li and Pi [Variable exponent functionals in image restoration, Appl. Math. Comput. 216 (2010), no. 3, 870–882].

We describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of N steps is of order 3 N/4 times a polynomial in N , and so the approach is greatly superior to direct counting techniques. We have enumerated walks of up to 39 steps. As a consequence, we are able to accurately estimate the critical point, cr...