{'fraction_non_alphanumeric': 0.022170361726954493, 'fraction_numerical': 0.002333722287047841, 'mean_word_length': 5.809523809523809, '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}}
Role of Interactions in Size-Dependent Curie Temperature of Magnetic Ultrathin Films

An arbitrary quantum spin Heisenberg model containing nearest neighbor antiferromagnetic and long-range dipole-dipole interactions, and single ion anisotropy is used to investigate the frustration effect in ultrathin magnetic films. Calculations using functional integral method and Gaussian spin fluctuation approximations showed that thicker films and larger spin S enhance the frustration critical ratio ε = |Js|/Jd where Js and Jd are antiferromagnetic exchange at surfaces and dipolar interaction strengths. The perpendicular positive (negative) anisotropy increases (reduces) this critical value. Results for spin S = 1/2 case are agreed with one of the temperature-dependent Green function method applied for quantum Heisenberg model in random phase approximation.