Related papers: Periodic striped states in Ising models with dipol…
This paper contains three types of results: 1. the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane, 2. the construction of nonlocal minimal surfaces…
It is known that, after a quench to zero temperature ($T=0$), two-dimensional ($d=2$) Ising ferromagnets with short-range interactions do not always relax to the ordered state. They can also fall in infinitely long-lived striped metastable…
Using reflection positivity techniques we prove the existence of minimizers for a class of mesoscopic free-energies representing 1D systems with competing interactions. All minimizers are either periodic, with zero average, or of constant…
It has recently been shown that one-dimensional Ising problems can have degenerate, disordered ground states (GSs) over a finite range of coupling onstants, ie, without `fine tuning'. The disorder is however of a special kind, consisting of…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
We compute the ground state of dipoles in a quasi-one-dimensional ring trap using few-body techniques combined with analytic arguments. The effective interaction between two dipoles depends on their center-of-mass coordinate and can be…
Statistical mechanical models with local interactions in $d>1$ dimension can be regarded as $d=1$ dimensional models with regular long range interactions. In this paper we study the critical properties of Ising models having $V$ sites, each…
Using the density matrix renormalization group, we study the possibility of real space checkerboard patterns arising as the ground states of the t-J model. We find that checkerboards with a commensurate (pi,pi) background are not low energy…
We examine correlation functions in the presence of competing long and short ranged interactions to find multiple correlation and modulation lengths. We calculate the ground state stripe width of an Ising ferromagnet, frustrated by an…
Motivated by recent experiments on cuprates with low-dimensional magnetic interactions, a new class of two-dimensional Ising models with short-range interactions and mobile defects is introduced and studied. The non-magnetic defects form…
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a…
We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of…
We present a innovative relationship between ground states of the Ising model and dimer coverings which sheds new light on the Ising Models with highly degenerated ground states and enables one to construct such models. Thanks to this…
Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field…
We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interactions. The model is defined in terms of an energy…
This paper mathematically studies membranes and filaments adhering to periodic patterned substrates in a one-dimensional model. The problem is formulated by the minimizing problem of an elastic energy with a contact potential on graph…
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
We consider testing for the parameters of Ferromagnetic Ising models. While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high…
We present a general method for obtaining a lower bound for the ground state entropy density of the Ising Model with nearest neighbor interactions. Then, using this method, and with a random coupling constant configuration, we obtain a…
The ground state phase diagram of the extended Hubbard model containing nearest and next-to-nearest neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local…