Abstract
The dimensional crossover in a spin-S nearest-neighbor Heisenberg antiferromagnet is discussed as it is tuned from a two-dimensional square lattice, of lattice spacing a, towards a spin chain by varying the width ${L}_{y}$ of a semi-infinite strip ${L}_{x}\ifmmode\times\else\texttimes\fi{}{L}_{y}$. For integer spins and arbitrary ${L}_{y}$, and for half integer spins with ${L}_{y}/a$ an arbitrary even integer, explicit analytical expressions for the zero temperature correlation length and the spin gap are given. For half integer spins and ${L}_{y}/a$ an odd integer, it is argued that the $c\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ behavior of the SU(2${)}_{1}$ Wess-Zumino-Witten fixed point is squeezed out as the width ${L}_{y}\ensuremath{\rightarrow}\ensuremath{\infty}$; here c is the conformal charge. The results specialized to $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ are applied to spin-ladder systems.
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