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The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…
We have obtained exact results for the Ising model on a hierarchical lattice with a scale-free degree distribution, high clustering coefficient, and small-world behavior. By varying the probability p of long-range bonds, the entire spectrum…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. In this thesis we…
We develop a tensor network-based method for calculating disorder-averaged expectation values in random spin chains without having to explicitly sample over disorder configurations. The algorithm exploits statistical translation invariance…
We investigate the laws of coarsening of a two-dimensional system of Ising spins evolving under single-spin-flip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from…
We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use…
The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner…
A closed expression is derived for the probability distribution of the transfer matrix of a particle moving in a one-dimensional system with delta-correlated, weak disorder. The change in the distribution as a function of wire length is…
Effects of the averaging over disorder realizations (samples) on the phase behavior are analyzed in terms of the mean field approximation for the random field Ising model with infinite range interactions. It is found that the averaging is…
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case…
The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in…
The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the $s = 1/2$ Ising lattice model with antiferromagnetic $1/r$…
In low temperature limit, we study electron counting statistics of a disordered conductor. We derive an expression for the distribution of charge transmitted over a finite time interval by using a result from the random matrix theory of…
In several observational contexts where different raters evaluate a set of items, it is common to assume that all raters draw their scores from the same underlying distribution. However, a plenty of scientific works have evidenced the…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
Probability distributions of the magnetic work are computed for the 2D Ising model by means of Monte Carlo simulations. The system is first prepared at equilibrium for three temperatures below, at and above the critical point. A magnetic…