... calculations^1.1

This argument was originally developed in collaboration with Dr. Timothy Edward Gallivan.

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... order^1.2

These calculations were developed in collaboration with Dr. André Cavalcanti Rocha Martins.

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... conditions^2.1

For a more complete understanding of the rest of this section it is useful, although not completely essential, to have some knowledge of the simulation techniques and some experience with stochastic simulations. This subject will be examined in detail in another volume of this series of books.

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... lattice^3.1

These arguments were developed in discussions with Dr. Timothy E. Gallivan and with Prof. Henrique Fleming.

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... phase^3.2

Note: the answer to this problem is currently unknown.

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... calculations^3.3

Note: the answer to this last question is currently unknown.

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