相关论文: Dobrushin Interfaces via Reflection Positivity

Reflection positivity (RP) is a property of Gibbs measures exhibited by a class of lattice spin systems that include the Ising, Potts and Heisenberg models. The RP property is useful because of its two basic consequences: infrared bound and…

Dobrushin (1972) showed that the interface of a 3D Ising model with minus boundary conditions above the $xy$-plane and plus below is rigid (has $O(1)$-fluctuations) at every sufficiently low temperature. Since then, basic features of this…

We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove…

The interface between the plus and minus phases in the low temperature 3D Ising model has been intensely studied since Dobrushin's pioneering works in the early 1970's established its rigidity. Advances in the last decade yielded the…

We provide a framework to study the interfaces imposed by Dobrushin boundary conditions on the half-plane version of the Ising model on random triangulations with spins on vertices. Using the combinatorial solution by Albenque, M\'enard and…

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the…

Understanding the contact between solid surfaces is a long standing problem which has a strong impact on the physics of many processes such as adhesion, friction, lubrication and wear. Experimentally, the investigation of solid/solid…

We discuss the apparent conflict between reflection positivity and positivity of the topological susceptibility in two-dimensional nonlinear sigma models and in four-dimensional gauge theories. We pay special attention to the fact that this…

In this paper we study a continuum version of the Potts model. Particles are points in R^d, with a spin which may take S possible values, S being at least 3. Particles with different spins repel each other via a Kac pair potential. In mean…

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost…

The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…

We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity $z$ and inverse temperature $\beta$. The…

Refraction at a smooth interface is accompanied by momentum transfer normal to the interface. We show that corrugating an initially smooth, totally reflecting, non-metallic interface provides a momentum kick parallel to the surface, which…

This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

Composite systems, where couplings are of two types, a combination of strong dilute and weak dense couplings of Ising spins, are examined through the replica method. The dilute and dense parts are considered to have independent canonical…

We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid…

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its…

We study the regularity of a diffusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and reflection between nearest neighbors. As our…

In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a…

The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…