Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper contains three types of results:the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane,the construction of nonlocal minimal surfaces which stay at a bounded distance from any given hyperplane,the reciprocal approximation of ground states for long-range Ising models and nonlocal minimal surfaces. In particular, we establish the existence of ground state solutions for long-range Ising models with planelike interfaces, which possess scale invariant properties with respect to the periodicity size of the environment. The range of interaction of the Hamiltonian is not necessarily assumed to be finite and also polynomial tails are taken into account (i.e. particles can interact even if they are very far apart the one from the other). In addition, we provide a rigorous bridge between the theory of long-range Ising models and that of nonlocal minimal surfaces, via some precise limit result.
Original languageEnglish
Pages (from-to)1401-1451
Number of pages51
JournalJournal of Statistical Physics
Volume167
Issue number6
DOIs
Publication statusPublished - 2017
Externally publishedYes

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minimal surfaces
Minimal surface
Ising model
Ising Model
hyperplanes
Ground State Solution
guy wires
Range of data
ground state
Hyperplane
Scale Invariant
periodic variations
polynomials
Periodicity
Ground State
Tail
approximation
Polynomial
Approximation
Interaction

Cite this

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title = "Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces",
abstract = "This paper contains three types of results:the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane,the construction of nonlocal minimal surfaces which stay at a bounded distance from any given hyperplane,the reciprocal approximation of ground states for long-range Ising models and nonlocal minimal surfaces. In particular, we establish the existence of ground state solutions for long-range Ising models with planelike interfaces, which possess scale invariant properties with respect to the periodicity size of the environment. The range of interaction of the Hamiltonian is not necessarily assumed to be finite and also polynomial tails are taken into account (i.e. particles can interact even if they are very far apart the one from the other). In addition, we provide a rigorous bridge between the theory of long-range Ising models and that of nonlocal minimal surfaces, via some precise limit result.",
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Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces. / Cozzi, Matteo ; Dipierro, Serena ; Valdinoci, E.

In: Journal of Statistical Physics, Vol. 167, No. 6, 2017, p. 1401-1451.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces

AU - Cozzi, Matteo

AU - Dipierro, Serena

AU - Valdinoci, E.

PY - 2017

Y1 - 2017

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AB - This paper contains three types of results:the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane,the construction of nonlocal minimal surfaces which stay at a bounded distance from any given hyperplane,the reciprocal approximation of ground states for long-range Ising models and nonlocal minimal surfaces. In particular, we establish the existence of ground state solutions for long-range Ising models with planelike interfaces, which possess scale invariant properties with respect to the periodicity size of the environment. The range of interaction of the Hamiltonian is not necessarily assumed to be finite and also polynomial tails are taken into account (i.e. particles can interact even if they are very far apart the one from the other). In addition, we provide a rigorous bridge between the theory of long-range Ising models and that of nonlocal minimal surfaces, via some precise limit result.

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