I suspect on thermodynamic grounds that this is false; the energy gap between the lowest and next-lowest energy configurations decreases exponentially in system size.
Indeed, Scott Aaronson did the experiment with soap bubbles (scroll down the page a bit) and found they often get stuck in local minima, just as one would expect.
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timeasmymeasure
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Date: 2010-03-07 04:17 am (UTC)Indeed, Scott Aaronson did the experiment with soap bubbles (scroll down the page a bit) and found they often get stuck in local minima, just as one would expect.