Cutting the cylinder into squares: the square form factor

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Packing equal squares into a large square

Let s(x) denote the maximum number of non-overlapping unit squares which can be packed into a large square of side length x. Let W (x) = x − s(x) denote the “wasted” area, i.e., the area not covered by the unit squares. In this note we prove that W (x) = O ( x √ 2)/7 log x ) . This improves earlier results of Erdős-Graham and Montgomery in which the upper bounds of W (x) = O(x) and W (x) = O(x(...

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Form Factor Representation of the Correlation Function of the Two Dimensional Ising Model on a Cylinder

The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are obtained both for the paramagnetic and ferromagnetic regions of coupling parameter. The peculiarities caused by finite size are analyzed. The scaling limit of th...

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ژورنال

عنوان ژورنال: Journal of High Energy Physics

سال: 2019

ISSN: 1029-8479

DOI: 10.1007/jhep03(2019)097