2018/08/01 by Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.PR
paper · pdf · doi:10.1007/s00220-019-03633-y
arxiv published 2018/08/01 · arxiv updated 2019/10/07 · openalex publication_date 2019/11/28 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28
Abstract The truncated two-point function of the ferromagnetic Ising model on \mathbb Zd <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:math> ( d≥ 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:mo>≥</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> ) in its pure phases is proven to decay exponentially fast throughout the ordered regime ( β gt;β c <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo>></mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math> and h=0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> ). Together with the previously known results, this implies that the exponential clustering property holds throughout the model’s phase diagram except for the critical point: (β ,h) = (β c,0) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>β</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> .