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<p>We consider <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {O}(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that at low temperatures, spin-spin correlations decay exponentially fast provided <i>n</i> is large enough. This answers a question of Ueltschi, who proved that for small <i>n</i> there is instead long-range order at low temperatures (for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(d\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>).</p>

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Exponential Decay in \(\mathcal {O}(n)\)-Invariant Quantum Spin Systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月25日

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  • J. E. Björnberg,
  • K. Ryan

摘要

We consider \(\mathcal {O}(n)\) O ( n ) -invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that at low temperatures, spin-spin correlations decay exponentially fast provided n is large enough. This answers a question of Ueltschi, who proved that for small n there is instead long-range order at low temperatures (for \(d\ge 3\) d ≥ 3 ).