相关论文: Periodic minimizers in 1D local mean field theory
We reprove a result by Ren and Wei concerning the periodicity of minimizers of a one-dimensional liquid drop model in the neutral case. Our proof works for general boundary conditions and also in the non-neutral case.
We consider a class of generalized antiferromagnetic local/nonlocal interaction functionals in general dimension, where a short range attractive term of perimeter type competes with a long range repulsive term characterized by a reflection…
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…
The purpose of this article is to extend the work by Anantharaman and Canc\`es [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density…
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…
We study the functional considered in~\cite{2011PhRvB..84f4205G,2014CMaPh.tmp..127G,GiuSeirGS} and a continuous version of it, analogous to the one considered in~\cite{GR}. The functionals consist of a perimeter term and a non-local term…
We study static 180 degree domain walls in infinite magnetic wires with bounded, $C^1$ and rotationally symmetric cross sections. We prove an existence of global minimizers for the energy of micromagnetics for any bounded $C^1$ cross…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
In this paper we complete the study of global minimizers of a forced, non autonomous, one dimensional, phase transition model, initiated in [8]. Motivated by the recent findings in [9], revealing new configurations of topological structures…
Motivated by the construction of time-periodic solutions for the three-dimensional Landau-Lifshitz-Gilbert equation in the case of soft and small ferromagnetic particles, we investigate the regularity properties of minimizers of the…
In this paper we consider the diffuse interface generalized antiferromagnetic model with local/nonlocal attractive/repulsive terms in competition studied in Daneri-Kerschbaum-Runa arXiv:1907.06419. The parameters of the model are denoted by…
We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the…
We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability $1-p$ and $p$, respectively, according to an i.i.d. random variable. We study minimizers of…
We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solutions are either periodic or quasiperiodic, depending on the…
We review the problem of determining the ground states of 2D Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling $J$ is…
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…
In this paper we study the existence of minimizers for interaction energies with the presence of external potentials. We consider a class of subharmonic interaction potentials, which include the Riesz potentials $|{\bf…
We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions are between $M$-neighbours for some $M\ge 2$ and are convex.…
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…
We prove the existence of minimizers in the class of negative definite measures on compact subsets of momentum space in the homogeneous setting under several side conditions (constraints). The method is to employ Prohorov's theorem. Given a…