Variational analysis of a two-dimensional frustrated spin system: Emergence and rigidity of chirality transitions

Marco Cicalese; Marwin Forster; Gianluca Orlando

doi:10.1137/19M1257305

Variational analysis of a two-dimensional frustrated spin system: Emergence and rigidity of chirality transitions

Marco Cicalese
, Marwin Forster
, Gianluca Orlando

Associate Professorship of Mathematical Continuum Mechanics

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We study the discrete-to-continuum variational limit of the J₁-J₃ spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. Carrying out the Γ-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.

Original language	English
Pages (from-to)	4848-4893
Number of pages	46
Journal	SIAM Journal on Mathematical Analysis
Volume	51
Issue number	6
DOIs	https://doi.org/10.1137/19M1257305
State	Published - 2019

Keywords

Calculus of variations
Chirality transitions
Frustrated lattice systems
Γ-convergence

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10.1137/19M1257305

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title = "Variational analysis of a two-dimensional frustrated spin system: Emergence and rigidity of chirality transitions",

abstract = "We study the discrete-to-continuum variational limit of the J1-J3 spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. Carrying out the Γ-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.",

keywords = "Calculus of variations, Chirality transitions, Frustrated lattice systems, Γ-convergence",

author = "Marco Cicalese and Marwin Forster and Gianluca Orlando",

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year = "2019",

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pages = "4848--4893",

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T1 - Variational analysis of a two-dimensional frustrated spin system

T2 - Emergence and rigidity of chirality transitions

AU - Cicalese, Marco

AU - Forster, Marwin

AU - Orlando, Gianluca

PY - 2019

Y1 - 2019

N2 - We study the discrete-to-continuum variational limit of the J1-J3 spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. Carrying out the Γ-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.

AB - We study the discrete-to-continuum variational limit of the J1-J3 spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. Carrying out the Γ-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.

KW - Calculus of variations

KW - Chirality transitions

KW - Frustrated lattice systems

KW - Γ-convergence

UR - https://www.scopus.com/pages/publications/85076389252

U2 - 10.1137/19M1257305

DO - 10.1137/19M1257305

M3 - Article

AN - SCOPUS:85076389252

SN - 0036-1410

VL - 51

SP - 4848

EP - 4893

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

Variational analysis of a two-dimensional frustrated spin system: Emergence and rigidity of chirality transitions

Abstract

Keywords

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