We have performed Monte Carlo simulations on the quantum Heisenberg antiferromagnet on the kagom\'e lattice with up to 72 spins. We have used the transfer-matrix Monte Carlo method, which enabled us to do efficient samplings at rather low temperatures where other methods suffer from serious sign problem. Specific-heat data exhibit the double peak. Results of the chirality and short-range spin correlations show no tendency of any magnetic ordering even at the lowest temperature we observed.
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Nakamura et al. (1995) studied this question.