相关论文: Gibbs Measures for Long-Range Ising Models
We considered a long-range Ising model under Glauber dynamics and calculated the difference from the mean-field approximation in a finite-size system using perturbation theory. To deal with the BBGKY hierarchy, we assumed that certain types…
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal…
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the…
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional…
A field-theoretical description of the behavior of compressible Ising systems with long-range interactions is presented. The description is performed in the two-loop approximation in three dimensions with the use of the Pade-Borel…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the…
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…
The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions…
These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.
In this paper, we consider an Ising model with three competing interactions on a triangular chandelier-lattice (TCL). We describe the existence, uniqueness, and non-uniqueness of translation-invariant Gibbs measures associated with the…
Interfaces in three-dimensional many-body systems can exhibit rich phenomena beyond the corresponding bulk properties. In particular, they can fluctuate and give rise to massless low energy degrees of freedom even in the presence of a…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-\delta}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a…
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 study the four dimensional site-diluted Ising model using finite-size scaling techniques. We explore the whole parameter space (density-coupling) in order to determine the Universality Class of the transition line. Our data are…
We study the non-equilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model -- a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent…
Consider the Ising model at low-temperatures and positive external field $\lambda$ on an $N\times N$ box with Dobrushin boundary conditions that are plus on the north, east, and west boundaries and minus on the south boundary. If $\lambda =…
In this paper we consider the Glauber dynamics for the one-dimensional Ising model with dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go to infinity with a suitable scaling. In this limit the…
We study the topology of fluid interfaces in the 3D Ising model in the rough phase. It turns out that such interfaces are accurately described as dilute gases of microscopic handles, and the stiffness of the interface increases with the…