We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges energy, and the resultant density states is modified continuously to produce locally flat histograms. This method permits us directly access free energy entropy, independent temperature, efficient for study both 1st order 2nd phase transitions. It should also be useful complex systems...

We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain very accurate estimate of the density states for classical statistical models. The is modified at each step when level visited produce flat histogram. By carefully controlling modification factor, we allow converge true value quickly, even large systems. From end walk, can thermodynamic quantities such as internal and specific heat capacity by calculating canonical averages any temperature. Using...

The examination of phase transitions and critical phenomena has dominated statistical physics for the latter half this century--there is a great theoretical challenge in solving special mechanical models. Additionally, beautiful experimental results have elucidated singularities (critical behavior) that occur transitions. Although few spectacular successes exact solution simple models occurred, interesting systems mostly proven to be intractable from analytic perspective. Because many...

We study the finite-size effects at a temperature-driven first-order transition by analyzing various moments of energy distribution. The distribution function for is approximated superposition two weighted Gaussian functions yielding quantitative estimates quantities and scaling form specific heat. rounding singularities shifts in location specific-heat maximum are analyzed characteristic features identified. predictions tested on ten-state Potts model dimensions carrying out extensive Monte...

The Wolff algorithm is now accepted as the best cluster-flipping Monte Carlo for beating ``critical slowing down.'' We show how this method can yield incorrect answers due to subtle correlations in ``high quality'' random number generators.

The phase diagrams of Ising antiferromagnets in a magnetic field $H$ are investigated for various values the ratio $R$ between nearest- and next-nearest-neighbor interaction. While meanfield approximations existing real-space renormalization-group treatments yield which sometimes even qualitatively incorrect, accurate results obtained from Monte Carlo calculations. For $R<0$ only an antiferromagnetically ordered exists. Its transition to disordered is first order temperatures below...

An importance-sampling Monte Carlo method is used to study $N\ifmmode\times\else\texttimes\fi{}N$ Ising square lattices with nearest-neighbor interactions and either free edges or periodic boundary conditions. The internal energy, specific heat, order parameter, susceptibility, near-neighbor spin-spin correlation functions of the finite are determined as a function $N$ extrapolated corresponding infinite-system values. effect size greater for in all cases. results agree well predictions...

Using both recently developed cluster-algorithm and histogram methods, we have carried out a high-resolution Monte Carlo study of static critical properties classical ferromagnetic Heisenberg models. Extensive simulations were performed at several temperatures in the region, using an improved cluster-updating scheme, on L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L simple-cubic body-centered-cubic systems with L\ensuremath{\le}40. Thermodynamic quantities as...

We describe a Monte Carlo algorithm for doing simulations in classical statistical physics different way. Instead of sampling the probability distribution at fixed temperature, random walk is performed energy space to extract an estimate density states. The can be computed any temperature by weighting states appropriate Boltzmann factor. Thermodynamic properties determined from suitable derivatives partition function and, unlike “standard” methods, free and entropy also directly. To...

Landau-Ginzburg-Wilson symmetry analyses and Monte Carlo calculations for the classical antiferromagnetic planar ($\mathrm{XY}$) model on a triangular lattice reveal wealth of interesting critical phenomena. From this simple arise zero-field transition to state long-range order, new mechanism spin disordering, point associated with possible universality class.

Critical, tricritical, and first-order wetting transitions are studied in a simple-cubic nearest-neighbor Ising model, with exchange J the bulk ${J}_{s}$ surface planes, by applying suitable fields H ${H}_{1}$. Monte Carlo calculations presented for systems of size L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D, thin film geometry D=40 layers two free L\ifmmode\times\else\texttimes\fi{}L surfaces, L ranging from L=10 to L=50. In addition, evidence prewetting layering...

The antiferromagnetic planar (XY) model on a triangular lattice is investigated using group-theoretical symmetry arguments combined with extensive Monte Carlo simulations and detailed finite-size-scaling analysis. This approach allows for systematic exploration of all possible symmetry-breaking transitions their associated critical behavior. entire magnetic-field--versus--temperature phase diagram deduced. A rich class new phenomena obtained, including the introduction multicritical point...

A Monte Carlo method is used to study $N\ifmmode\times\else\texttimes\fi{}N\ifmmode\times\else\texttimes\fi{}N$ simple-cubic Ising lattices with periodic boundary conditions and free edges. For both types of the position specific-heat maximum varies for large $N$ as $a{N}^{\ensuremath{-}\ensuremath{\lambda}}$, where $\ensuremath{\lambda}$ has scaling value $\ensuremath{\lambda}={\ensuremath{\nu}}^{\ensuremath{-}1}$. Both thermal magnetic properties are shown obey finite-size scaling. The...

While a nonzero spontaneous magnetization $m$ cannot exist in $d=2$ Heisenberg spin system, it is possible that phase transition associated with divergent susceptibility occurs at the Stanley-Kaplan temperature ${T}_{c}^{\mathrm{SK}}$. The crossover from this special isotropic case to anisotropic (Ising) behavior studied using Monte Carlo technique. classical model Hamiltonian...

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Carlo renormalization group, and series expansion have provided precise information about phase transition. Using simulation that employs Wolff cluster flipping algorithm with both 32-bit 53-bit random number generators data analysis histogram reweighting quadruple precision arithmetic, we investigated critical behavior of simple cubic Model, lattice sizes ranging from ${16}^{3}$...

In a magnetic field along $〈111〉$ axis, dysprosium aluminum garnet (DAG) closely resembles two-sublattice Ising antiferromagnet, and it undergoes transition to the paramagnetic state without spin flopping. To investigate nature of this transition, high-resolution measurements have been made isothermal magnetization specific heat ${C}_{H}$ as function temperature from 1.1 4.2 \ifmmode^\circ\else\textdegree\fi{}K in fields up 14 kOe. A number additional also down 0.5 between 8...