{'fraction_non_alphanumeric': 0.0299625468164794, 'fraction_numerical': 0.0, 'mean_word_length': 5.369047619047619, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Erratum: Elastic modes, phase fluctuations, and long-range order in type-II superconductors

We consider the effect of thermal fluctuations on the phase of the superconducting order parameter of the Abrikosov flux-line-lattice state of a type-II superconductor. While in the electrodynamic gauges usually chosen there are apparently divergent phase fluctuations, we show that the gauge-invariant phase has a finite average value. Thus, conventional superconducting long-range order is present in a three-dimensional flux line lattice.