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We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $pin[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c sim 0.103$ compared to the concentration $p_nsim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.
Domain-wall free-energy $delta F$, entropy $delta S$, and the correlation function, $C_{rm temp}$, of $delta F$ are measured independently in the four-dimensional $pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $theta$, the frac
We apply generalisations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional $pm 1$ random-bond Ising model. The behaviour of the model is determined by the te
We present results on the first excited states for the random-field Ising model. These are based on an exact algorithm, with which we study the excitation energies and the excitation sizes for two- and three-dimensional random-field Ising systems wit
The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these algorithm by various methods in order to analyze low-ene
The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two multifract