{'fraction_non_alphanumeric': 0.023952095808383235, 'fraction_numerical': 0.004790419161676647, 'mean_word_length': 4.687074829931973, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, '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}}
On the changeover in the transition nature of local-interaction Potts models

A combinatorial approach is used to study the critical behavior of a q-state Potts model with a round-the-face interaction. Using this approach, it is shown that the transition is of first order for q > 3. A second order transition is numerically detected for q = 2. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer qc ≤ 3. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is qc = 4. Under a conceivable assumption, an exact expression for the first order transition critical temperature is additionally derived.