Related papers: The restriction of the Ising model to a layer
The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film…
Using a Ginzburg-Landau model, we study the phase transition behavior of compressible Ising systems at constant volume by varying the temperature $T$ and the applied magnetic field $h$. We show that two phases can coexist macroscopically in…
We discuss a geometrical interpretation of the Z-invariant Ising model in terms of isoradial embeddings of planar lattices. The Z-invariant Ising model can be defined on an arbitrary planar lattice if and only if certain paths on the…
We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties…
The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…
The critical temperature of layered Ising models on triangular and honeycomb lattices are calculated in simple, explicit form for arbitrary distribution of the couplings.
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
We consider the diagonal susceptibility of the isotropic 2D Ising model for temperatures below the critical temperature. For a parameter k related to temperature and the interaction constant, we extend the diagonal susceptibility to complex…
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an…
We consider the low temperature expansion for the Ising model on $\Z^d$, $d \ge 2$, with ferromagnetic nearest neighbor interactions in terms of Peierls contours. We prove that the expansion converges for all temperatures smaller than $C d…
We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Koteck\'y, and clear evi…
It is analytically shown that the one-dimensional Ising model with Glauber dynamics exhibits short time memory effects when submitted to an abrupt change in the temperature. These effects are qualitatively similar to those experimentally…
L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass…
This work explores the possibilities of the Gibbs-Bogoliubov-Feynman variational method, aiming at finding room for designing various drawing schemes. For example, mean-field approximation can be viewed as a result of using site-independent…
In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…
In contrast to the infinite chain, the low-temperature expansion of a one-dimensional free-field Ising model has a strong dependence on boundary conditions. I derive explicit formula for the leading term of the expansion both under open and…
We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…
In the present paper, the Ising model with mixed spin-(1,1/2) is considered on the second order Cayley tree. A construction of splitting Gibbs measures corresponding the model is given which allows to establish the existence of the phase…
We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs-Thomson formula for the deviation of the pressure and the…