{'fraction_non_alphanumeric': 0.007736943907156673, 'fraction_numerical': 0.0, 'mean_word_length': 4.954022988505747, '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}}
Interfaces in a random medium and replica symmetry breaking

The authors develop a variational approach for studying interfaces and other manifolds in a disordered quenched medium. The method may be applied to problems which range from directed polymers to the interface of an Ising model in a random magnetic field. They find that replica symmetry is spontaneously broken and the results of the Flory approximation are recovered in a simple way. Corrections to this approximation may be computed in a systematic way.