Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random $k$-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as "replica symmetry" in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random $k$-SAT model at low temperature for clause/variable densities below but close to the satisfiability threshold.

翻译：我们根据统计物理的预测,证明信仰传播信息传导算法在所有条款/可变密度和所有不长距离相关条件得到满足的逆向温度中都非常接近随机美元/可变密度模型的分割功能。在物理学语言中,这一条件被称为“重复对称性”。根据这一结果,我们推断,随机美元/可变密度模型的对称性断裂阶段过渡发生在低温度下但接近可对称性临界值的随机美元/可变密度模型中。