| 1. | Dimensionless coupling constants are the technical hallmark for the upper critical dimension.
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| 2. | Above the critical dimension the instability drives to a non-uniform black ring phase.
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| 3. | In Mukhamel's analysis of the isotropic Lifschitz point, the critical dimension is 8.
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| 4. | Still, there was something missing _ a critical dimension that was being missed.
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| 5. | The first and, in many ways, most critical dimension is space.
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| 6. | The upper critical dimension may be read off at the E _ 1-axis ..
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| 7. | Below the lower critical dimension, there is no field theory corresponding to the model.
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| 8. | The dimension is called the upper critical dimension above which excluded volume is negligible.
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| 9. | These anomalous contributions to the effective critical exponents vanish at the upper critical dimension.
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| 10. | In the Ising model, the critical dimension is 4.
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