We use a recently developed cluster algorithm for the Baxter–Wu model to study characteristic features of its behavior. Magnetic scaling properties of the model are investigated for second-order phase transitions. We improve significantly the accuracy of Monte Carlo simulation results and we...

Kasteleyn's treatment of the hamiltonian walk problem on lattice graphs is briefly reviewed. The asymptotic behaviour of the number of hamiltonian walks on the kth covering of a closed oriented lattice graph is expressed in terms of the asymptotic behaviour of the number of oriented trees on the...

We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the Metropolis algorithm. We consider interactions in the range where...

The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of the Wang-Landau algorithm. The simulations are...

The three-dimensional bimodal random-field Ising model is investigated using the N-fold version of the Wang-Landau algorithm. The essential energy subspaces are determined by the recently developed critical minimum energy subspace technique, and two implementations of this scheme are utilized....

We investigate, by means of extensive Monte Carlo simulations, the magnetic critical behavior of the three-dimensional bimodal random-field Ising model at the strong disorder regime. We present results in favor of the two-exponent scaling scenario, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\bar{\eta}$</EquationSource> </InlineEquation>=2η, where η and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\bar{\eta}$</EquationSource> </InlineEquation>...</equationsource></inlineequation></equationsource></inlineequation>

The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM). The present approach generalizes our earlier...

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume–Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the...

Using a Wang–Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R=Jnnn/Jnn=1, for which the pure model...

The complications encountered in direct renormalization approaches for the self-avoiding walk problem are discussed. Using a decimation transformation on the square lattice, sequences of approximants to the critical exponent ν and to the inverse connective constant Kc(1Kc = μ) are obtained.