Search results for "Ising Model"
showing 10 items of 241 documents
Carrier-induced ferromagnetism in two-dimensional magnetically doped semiconductor structures
2021
We show theoretically that the magnetic ions, randomly distributed in a two-dimensional (2D) semiconductor system, can generate a ferromagnetic long-range order via the RKKY interaction. The main physical reason is the discrete (rather than continuous) symmetry of the 2D Ising model of the spin-spin interaction mediated by the spin-orbit coupling of 2D free carriers, which precludes the validity of the Mermin-Wagner theorem. Further, the analysis clearly illustrates the crucial role of the molecular field fluctuations as opposed to the mean field. The developed theoretical model describes the desired magnetization and phase-transition temperature ${T}_{c}$ in terms of a single parameter, na…
Critical properties and finite-size effects of the five-dimensional Ising model
1985
Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length ξ (the temperature variation of which near the critical temperatureT c is ξ∝|1-T/T c |−1/2), but rather with a “thermodynamic length”l (withl∝|1-T/T c |−2/d ,d=5 here). The susceptibility (extrapolated to the thermodynamic …
Finite-size tests of hyperscaling.
1985
The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.
Monte Carlo simulations of the 2d-Ising model in the geometry of a long stripe
2011
Abstract The two-dimensional Ising model in the geometry of a long stripe can be regarded as a model system for the study of nanopores. As a quasi-one-dimensional system, it also exhibits a rather interesting “phase behavior”: At low temperatures the stripe is either filled with “liquid” or “gas” and “densities” are similar to those in the bulk. When we approach a “pseudo-critical point” (below the critical point of the bulk) at which the correlation length becomes comparable to the length of the stripe, several interfaces emerge and the systems contains multiple “liquid” and “gas” domains. The transition depends on the size of the stripe and occurs at lower temperatures for larger stripes.…
Ising model universality for two-dimensional lattices
1993
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80\,000 sites. By applying reweighting techniques and finite-size scaling analyses to time-series data near criticality, we obtain unambiguous support that the critical exponents for the random lattice agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.
The Ising transition in 2D simplicial quantum gravity - can Regge calculus be right?
1995
We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to $512^2$ vertices. For the constant area ensemble and the $dl/l$ functional measure we definitively can exclude the critical exponents of the Ising phase transition as predicted for dynamically triangulated surfaces. We rather find clear evidence that the critical exponents agree with the Onsager values for static regular lattices, independent of the coupling strength of an $R^2$ interaction term. For exploratory simulations using the lattice version of the Misner measure the situation is less clear.
Tensor Network Annealing Algorithm for Two-Dimensional Thermal States
2019
Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark we …
Dynamic percolation transition induced by phase separation: A Monte Carlo analysis
1987
The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider “quenching experiments,” where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki “spinexchange” dynamics. Analyzing the distributionnl(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly l…
Interface Localization-Delocalization in a Double Wedge: A New Universality Class with Strong Fluctuations and Anisotropic Scaling
2002
Using Monte Carlo simulations and finite-size scaling methods we study ``wetting'' in Ising systems in a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ pore with quadratic cross section. Antisymmetric surface fields ${H}_{s}$ act on the free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces of the opposing wedges, and periodic boundary conditions are applied along the $y$ direction. In the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$, ${L}_{y}/{L}^{3}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$, the system exhibits a new type of phase transition, which is the analog of the ``filling transition'' that occurs in a single wedge. It is charac…
The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers
1989
Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the …