Search results for "ISING"
showing 10 items of 1141 documents
Realization of a two-dimensional Ising system: Deuterium physisorbed on krypton-preplated graphite
2004
Volumetric adsorption isotherm, calorimetric, and neutron diffraction measurements were used to characterize the quantum system ${\mathrm{D}}_{2}$ coadsorbed on graphite preplated by a monolayer of Kr. From the results obtained by these methods a detailed phase diagram of the complete submonolayer coverage range up to the initial stages of bilayer formation could be constructed. The dominant feature of the phase diagram is a commensurate $(1\ifmmode\times\else\texttimes\fi{}1)[\frac{1}{2}]$ structure, which was determined by neutron diffraction. Three phase transitions of this phase were studied: The order-disorder transition at the critical point which, according to the influence of the co…
Character of the Phase Transition in Thin Ising Films with Competing Walls
1995
By extensive Monte Carlo simulations of a lattice gas model we have studied the controversial nature of the gas-liquid transition of a fluid confined between two parallel plates that exert competing surface fields. We find that the transition is shifted to a temperature just below the wetting transition of a semi-infinite fluid but belongs to the two-dimensional Ising universality class. In between this new type of critical point and bulk criticality, a response function ${x}_{\mathrm{nn}}^{max}$ varying exponentially with $D$ is observed, $\frac{2 \mathrm{ln}{\ensuremath{\chi}}_{\mathrm{nn}}^{max}}{D}={\ensuremath{\ell}}^{\ensuremath{-}1}$, where $\ensuremath{\ell}$ is a new length charact…
Some Important Recent Developments of the Monte Carlo Methodology
2002
Roughly at the time (1987) when the manuscript for the first three chapters of the present book was completed, several breakthroughs occurred. They had a profound influence on the scope of Monte Carlo simulations in statistical physics, particularly for the study of phase transitions in lattice models.
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
2001
Abstract A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one c…
Study of the confined Ising magnet with long-range competing boundary fields
2005
We present extensive Monte Carlo simulations of the Ising film confined in an L × M geometry () in the presence of long-range competing magnetic fields h(n) = h1/n3(n = 1,2,...,L) which are applied at opposite walls along the M-direction. Due to the fields, an interface between domains of different orientations that runs parallel to the walls forms and can be located close to one of the two surfaces or fluctuate in the centre of the film (localization–delocalization transition). This transition is the precursor of the wetting phase transition that occurs in the limit of infinite film thickness () at the critical curve Tw(h1). For T<Tw(h1) (T≥Tw(h1)) such an interface is bound to (unbound fr…
Monte Carlo study of surface phase transitions in the three-dimensional Ising model.
1990
We present the results of extensive Monte Carlo simulations of phase transitions and critical behavior at the surface of a simple cubic Ising model. Profiles of the magnetization and internal energy are determined as a function of the distance from the surface, and we extract surface and bulk properties as a function of temperature and surface coupling ${\mathit{J}}_{\mathit{s}}$. The surface-bulk multicritical point is located with improved precision, ${\mathit{J}}_{\mathit{s}}$/J=1.52\ifmmode\pm\else\textpm\fi{}0.02, and crossover behavior is studied. New estimates for critical exponents are extracted, ${\ensuremath{\gamma}}_{1}$=0.78\ifmmode\pm\else\textpm\fi{}0.06, ${\ensuremath{\gamma}…
Surface effects on phase transitions of modulated phases and at Lifshitz points: A mean field theory of the ANNNI model
1999
The semi-infinite axial next nearest neighbor Ising (ANNNI) model in the disordered phase is treated within the molecular field approximation, as a prototype case for surface effects in systems undergoing transitions to both ferromagnetic and modulated phases. As a first step, a discrete set of layerwise mean field equations for the local order parameter mn in the nth layer parallel to the free surface is derived and solved, allowing for a surface field H1 and for interactions JS in the surface plane which differ from the interactions J0 in the bulk, while only in the z-direction perpendicular to the surface competing nearest neighbor ferromagnetic exchange (J1) and next nearest neighbor an…
Monte Carlo Methods: a powerful tool of statistical physics
1998
Statistical mechanics of condensed matter systems (solids, fluids) tries to express macroscopic equilibrium properties of matter as averages computed from a Hamiltonian that expresses interactions of an atomistic many body system. While analytic methods for most problems involve crude and uncontrolled approximations, the Monte Carlo computer simulation method allows a numerically exact treatment of this problem, apart from “statistical errors” which can be made as small as desired, and the systematic problem that a system of finite size is treated rather than the thermodynamic limit. However, the simulations of phase transitions then elucidate how a symmetry breaking arises via breaking of …
Critical behavior of active Brownian particles
2017
We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\…
Theory of orientational glasses models, concepts, simulations
1992
Abstract This review describes the various attempts to develop a theoretical understanding for ordering and dynamics of randomly diluted molecular crystals, where quadrupole moments freeze in random orientations upon lowering the temperature, as a result of randomness and competing interactions. While some theories attempt to model this freezing into a phase with randomly oriented quadrupole moments in terms of a bond-disorder concept analogous to the Edwards-Anderson model of spin glasses, other theories attribute the freezing to random field-like terms in the Hamiltonian. While models of the latter type have been studied primarily by microscopic molecular field-type treatments, the former…