A plane of weakly coupled Heisenberg chains: theoretical arguments and numerical calculations

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Abstract
The S= 1/2 , nearest-neighbour, quantum Heisenberg antiferromagnet on the square lattice with spatially anisotropic couplings is reconsidered, with particular attention to the following question: at T=0, does Neel order develop at infinitesimal interchain coupling, or is there a non-zero critical coupling? A heuristic renormalization-group argument is presented which suggests that previous theoretical answers to this question are incorrect or at least incomplete, and that the answer is not universal but rather depends on the microscopic details of the model under consideration. Numerical investigations of the nearest-neighbour model are carried out via zero-temperature series expansions about Ising and dimer Hamiltonians. The results are entirely consistent with a vanishing critical interchain coupling ratio Rc; if Rc is finite, it is unlikely to substantially exceed 0.02.
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