Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum Spontaneous Magnetization and Nambu-Goldstone Mode   We study quantum antiferromagnetic Heisenberg models on a hypercubic lattice.
We prove the following three theorems without any assumption: (i) The
spontaneous magnetization which is obtained by applying the infinitesimally
weak symmetry breaking field is equal to the maximum spontaneous magnetization
at zero or non-zero low temperatures. (ii) When the spontaneous magnetization
is non-vanishing at zero temperature, there appears a gapless excitation,
Nambu-Goldstone mode, above an infinite-volume pure ground state. (iii) When
the spontaneous magnetization is non-vanishing at zero or non-zero low
temperatures, the transverse correlation in the infinite-volume limit exhibits
a Nambu-Goldstone-type slow decay.

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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci