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mathematical-physics / Statistical mechanics; Berezinskii-Kosterlitz-Thouless transition

The Kosterlitz essential singularity of the XY correlation length

Theorem 1.1: there is AXY∈(0,∞)A_{XY}\in(0,\infty) with lim⁡b↑bcbc−b log⁡ξ(b)=AXY\lim_{b\uparrow b_c}\sqrt{b_c-b}\,\log\xi(b)=A_{XY}, for the square-lattice nearest-neighbor cosine model. The constant is expressed through the block construction and is not evaluated. It does not cover other lattices, the Villain model, the behaviour of the susceptibility, or corrections beyond the leading order.

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mathematical-physicsOct 5, 2026Significance 48/100Registry: unreviewed

The Kosterlitz essential singularity of the XY correlation length

Prior state unknown→proved

Theorem 1.1: there is AXY∈(0,∞)A_{XY}\in(0,\infty) with lim⁡b↑bcbc−b log⁡ξ(b)=AXY\lim_{b\uparrow b_c}\sqrt{b_c-b}\,\log\xi(b)=A_{XY}, for the square-lattice nearest-neighbor cosine model. The constant is expressed through the block construction and is not evaluated. It does not cover other lattices, the Villain model, the behaviour of the susceptibility, or corrections beyond the leading order.

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Theorem 1.1: there is AXY∈(0,∞)A_{XY}\in(0,\infty) with lim⁡b↑bcbc−b log⁡ξ(b)=AXY\lim_{b\uparrow b_c}\sqrt{b_c-b}\,\log\xi(b)=A_{XY}, for the square-lattice nearest-neighbor cosine model. The constant is expressed through the block construction and is not evaluated. It does not cover other lattices, the Villain model, the behaviour of the susceptibility, or corrections beyond the leading order.

Theorem 1.1: there is AXY∈(0,∞)A_{XY}\in(0,\infty) with lim⁡b↑bcbc−b log⁡ξ(b)=AXY\lim_{b\uparrow b_c}\sqrt{b_c-b}\,\log\xi(b)=A_{XY}, for the square-lattice nearest-neighbor cosine model. The constant is expressed through the block construction and is not evaluated. It does not cover other lattices, the Villain model, the behaviour of the susceptibility, or corrections beyond the leading order.

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