We demonstrate that the Ising model on a general triangular graph with three distinct couplings ${K}_{1}$, ${K}_{2}$, and ${K}_{3}$ corresponds to an affine transformed conformal field theory (CFT). Full invariance of $c=1/2$ minimal CFT is restored by introducing metric lattice through map $\mathrm{sinh}(2{K}_{i})={\ensuremath{\ell}}_{i}^{*}/{\ensuremath{\ell}}_{i}$ which relates critical rati...

The Ising model is one of the standard models in statistical physics. Since 1969 more than 12000 publications appeared using this model. In 1996 Ernst Ising celebrated his 96th birthday. Some biographical notes and milestones of the development of the Ising model are given. the son of the merchant Gustav Ising and his wife Thekla, nee Löwe. The family moved to Bochum (Westfall). Ernst Ising com...

We consider by means of Monte Carlo simulations the relaxation in the paramagnetic phase of the anti-ferromagnetic Ising model on a triangular lattice and of a fully-frustrated Ising model on a square lattice. In contradistinction to previous studies of the second model, we show that spin-spin correlation functions do not decay with a stretched-exponential law at low temperature but that both m...

The investigation of evolutionary algorithms as adaptation schemes has a long history starting with Holland (1975). The Ising model from physics leads to a variety of different problem instances and it is interesting to investigate how simple evolutionary algorithms cope with these problems. A theoretical analysis is known only for the Ising model on the ring and partially for the Ising model o...

We consider Glauber{type dynamics for two dimensional disordered magnets of Ising type. We prove that, if in equilibrium the disorder{averaged innuence of the boundary condition is suuciently small, then the corresponding Glauber dynamics is ergodic with probability one and the disorder{averaged of time{autocorrelations decays like e ?m(log t) 2. For the standard dilute Ising ferromagnet with i...

We study the site-diluted Ising model in two dimensions with Monte Carlo simulations. Using nite-size scaling techniques we compute the critical exponents observing deviations from the pure Ising ones. The diierences can be explained as the eeects of logarithmic corrections, without requiring to change the Universality Class.

-The dynamical critical exponent z of he two-dimensional Ising model with sequential-flip heat-bath dynamics is numerically estimated to be 2.2, which agrees with that of Metropolis dynamics. The dedicated machine "m-TIS" designed and constructed by the present authors is used for the simulations. The Monte barlo simulation is one of the most powerful methods in studying cooperative phenomena [...

Meik Hellmund1,3,* and Wolfhard Janke2,3,† 1Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany 2Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany 3Centre for Theoretical Sciences (NTZ) of the Centre for Advanced Study (ZHS), Universität Leipzig, Emil-Fuchs-Straße 1, D-04105 Leipzig, Germany Received 13 J...