Search results for "Ising Model"

A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields

2005

We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension 2L + 1. Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit L → ∞, the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.

Critical behavior of the surface-layer magnetization at the extraordinary transition in the three-dimensional Ising model.

1990

We have used a vectorized multispin-coding Monte Carlo method to determine the behavior of the surface-layer magnetization ${\mathit{m}}_{1}$ at the bulk transition in a simple-cubic Ising film with strongly enhanced surface coupling, i.e., at the extraordinary transition. In contrast to recent renormalization-group calculations we find no evidence for a discontinuous slope in the temperature dependence of ${\mathit{m}}_{1}$; the data are consistent with a free-energy-like (T-${\mathit{T}}_{\mathit{c}}$${)}^{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ behavior plus background terms.

Universal critical behavior of curvature-dependent interfacial tension.

2011

From the analysis of Monte Carlo simulations of a binary Lennard-Jones mixture in the coexistence region, we provide evidence that the curvature dependence of the interfacial tension can be described by a simple theoretical function σ(R)ξ(2)=C(1)/[1+C(2)(ξ/R)(2)], where ξ is the correlation length and R is the droplet radius. The universal constants C(1) and C(2) are estimated. In the model, a Tolman length is strictly absent, but, since its critical behavior is believed to be much weaker than ξ, we argue that it only provides a correction to scaling and does not affect the leading critical behavior, which should be described by the above function for any system in the Ising universality cl…

Monte Carlo studies of anisotropic surface tension and interfacial roughening in the three-dimensional Ising model.

1989

Extensive Monte Carlo simulations of the simple cubic Ising model with nearest-neighbor ferromagnetic interactions with a tilted interface are presented for a wide range of lattice size L, temperature T, and tilt angles \ensuremath{\theta}. The anisotropic interfacial tension is studied in detail. From the small-angle data, we obtain the step free energy density ${f}_{S}$(T,L). Finite-size scaling of the step free energy density is discussed and used to probe the predicted temperature dependence of the correlation length near and above the roughening transition. The square-root temperature dependence predicted by solid-on-solid model calculations is exhibited. Finite-size scaling implies th…

Phase separation in thin films: Effect of temperature gradients

2013

We study the phase-separation kinetics of a binary (AB) mixture confined in a thin film of thickness D with a temperature gradient. Starting from a Kawasaki-exchange kinetic Ising model, we use a master-equation approach to systematically derive an extension of the Cahn-Hilliard model for this system. We study the effect of temperature gradients perpendicular to the film with "neutral" (no preference for either A or B) surfaces. We highlight the rich phenomenology and pattern dynamics which arises from the interplay of phase separation and the temperature gradient.

Thermal properties of the tetrahydrate series MtM(M'EDTA)2·4H2O {Mt, M, M' = Co(II), Ni(II), Zn(II)}

1992

Abstract We report on the specific heat data of the ordered bimetallic compounds CoCo(CoEDTA) 2 ·4H 2 O and CoCo(NiEDTA) 2 ·4H 2 O in the temperature range 1.5−15 K. The magnetic specific heat is analyzed from an Ising model that assumes three different magnetic sublattices exchange-coupled by two distinct magnetic interactions, as well as local anisotropies on tetrahedral Co and octahedral Ni sites.

Finite Size Scaling Tools for the Study of Interfacial Phenomena and Wetting

2019

In this chapter, we use the word “interface” in the sense of a boundary between coexisting bulk phases (in thermal equilibrium). An example is the interface between liquid (e.g. water) and gas phases (water vapor) but also interfaces between fluid and solid phases (e.g. water and ice) can be considered, as well as interfaces between coexisting solid phases. The generic example are “domain walls” in magnets, separating domains with opposite orientation of the magnetization, a case that can already be studied in the framework of the simple Ising model (Chaps. 2 and 3) where one has spins on the sites of a rigid perfect lattice pointing up or down.

2019

Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…

Interfaces between coexisting phases in polymer mixtures: What can we learn from Monte Carlo simulations?

1999

Symmetric binary polymer mixtures are studied by Monte Carlo simulation of the bond fluctuation model, considering both interfaces between coexisting bulk phases and interfaces confined in thin films. It is found that the critical behavior of interfacial tension and width is compatible with that of the Ising model, as expected from the universality principle. In the strong segregation limit, only qualitative but not quantitative agreement with the self-consistent field (SCF) theory is found. It is argued that the SCF theory requires √ 6 X √D for short-range forces, in agreement with experiment.

Quenched and annealed free energies

1984

This paper gives a simple exposition of the Nishimori method to solve certain quenched, random bond spin-glass models. It allows a transparent physical interpretation in terms of annealed systems. As an application a special solution of the Sherrington-Kirkpatrick model with a discrete probability distribution is obtained and shown to agree with the solution for the Gaussian case. This substantiates the claim that the averaged free energy does not depend on the details of the probability distribution Expose simple de la methode de Nishimori pour resoudre certains modeles de verres de spin avec interactions aleatoires. Interpretation transparente en termes de systemes recuits. Presentation d…