Related papers: A self-consistent Ornstein-Zernike approximation f…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with $1 \leq q <4$ that also applies in its near-critical regime. In particular, we prove an asymptotic formula for the two-point function which holds…
In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random fields on the tricritical phase diagram of the spin-1 Ising model…
This thesis contains three main parts, which are largely independent. In the first part we deal with the boundary bootstrap in supersymmetric factorized scattering theory. We give a description of supersymmetry in the case when the space is…
We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice with periodic boundary conditions. The finite size scaling relation for the…
In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due…
The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…
We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field…
In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the…
We study canonical-equilibrium properties of Random Field $O(n)$ Models involving classical continuous vector spins of $n$ components with mean-field interactions and subject to disordered fields acting on individual spins. To this end, we…
A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…
We consider spin models on complex networks frequently used to model social and technological systems. We study the annealed ferromagnetic Ising model for random networks with either independent edges (Erd\H{o}s-R\'enyi), or with prescribed…
Over the years, the Self-Consistent Harmonic Approximation (SCHA) has been successfully utilized to determine the transition temperature of many different magnetic models, particularly the Berezinskii-Thouless-Kosterlitz transition in…
We report a high-precision numerical estimation of the critical exponent $\alpha$ of the specific heat of the random-field Ising model in four dimensions. Our result $\alpha = 0.12(1)$ indicates a diverging specific-heat behavior and is…
We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function in the general context of finite range Ising type models on Z^d. The proof relies in an essential way on the a-priori knowledge of the strict…
The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the…
The short-time critical dynamics of propagation of damage in the Ising ferromagnet in two dimensions is studied by means of Monte Carlo simulations. Starting with equilibrium configurations at $T= \infty$ and magnetization $M=0$, an initial…
We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This…