Related papers: Logarithmic Correlations in Quenched Random Magnet…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…
It is well-known that the semi-circle law, which is the limiting distribution in the Wigner theorem, is the minimizer of the logarithmic energy penalized by the second moment. A very similar fact holds for the Girko and Marchenko--Pastur…
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy \[H_n=\sum_{1\le j<k\le n}\omega_j\omega_k1_{\{S_j=S_k\}}\] of the polymer $\{S_1,...,S_n\}$ equipped with random…
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…
We present a model of polymer growth and diffusion with frustration mechanisms for density increase and with diffusion rates of Arrhenius form with mass-dependent energy barriers Gamma(m) ~ (m-1)^gamma. It shows non-universal logarithmic…
We define a notion of logarithmic, Coulomb and Riesz interactions in any dimension for random systems of infinite charged point configurations with a uniform background of opposite sign. We connect this interaction energy with the…
Monte carlo simulation of paths of a large number of impinging electrons in a multi-layered solid allows to define area of spreading electrons (A) to capture overall behavior of the solid. This parameter 'A' follows power law with electron…
We study entanglement properties of systems with spontaneously broken continuous symmetry. We find that in addition to the expected area law behavior, the entanglement entropy contains a subleading contribution which diverges…
It is shown that the ratios of the quenched averaged three and four-point correlation functions of the local energy density operator to the connected ones in the random-bond Ising model approach asymptotically to some $universal$ functions.…
We introduce a random walk in random environment associated to an underlying directed polymer model in $1+1$ dimensions. This walk is the positive temperature counterpart of the competition interface of percolation and arises as the limit…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
The slow dynamics for a colloidal suspension of particles interacting with a hard-core repulsion complemented by a short-ranged attraction is discussed within the frame of mode-coupling theory for ideal glass transitions for parameter…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
A general kind of models with hierarchically constrained dynamics is shown to exhibit logarithmic anomalous relaxation, similarly to a variety of complex strongly interacting materials. The logarithmic behavior describes most of the decay…
A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The…
We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This…
Exploring the lowest energy configurations of a quantum system is consistent with the counting statistics of the frequently appeared states from quenching dynamics. By studying the Little-Parks periodicities in a multiply-connected…
A particularly interesting feature of nonrelativistic quantum mechanics is the monogamy laws of entanglement. Although the monogamy relation has been explored extensively in the last decade, it is still not clear to what extent a given…
The some dynamic properties of a random heteropolymer in the condensed state are studied in the mode coupling approximation. In agreement with recent report a dynamic friction increasing is predicted for the random heteropolymer with…