关键词: 平均场近似, 伊辛模型, 相变

Abstract: To address the common pedagogical dilemma in undergraduate statistical physics where conventional meanfield theory erroneously predicts a finitetemperature phase transition for the onedimensional Ising model, this article proposes the introduction of the more accurate hardspin meanfield theory (HSMFT) into the curriculum. The paper elaborates on the theoretical framework of HSMFT, which retains the discrete nature of spins and establishes selfconsistent equations by statistically averaging over all possible microconfigurations of the neighbors. Using the twodimensional Ising model as a detailed example, we stepbystep demonstrate the derivation process and briefly present results for one and three dimensions, confirming the dual superiority of HSMFT in both qualitative correctness and quantitative accuracy. As an advanced application, we extend HSMFT to the sitediluted Ising model. By introducing a double averaging over the number of active neighbors, we obtain the phase diagram and discuss the magnetic critical concentration, thereby illustrating the theory's capability in handling disordered systems and its pedagogical value. This approach provides students with a coherent and profound theoretical picture spanning from pure to disordered systems.

Key words: meanfield approximation, Ising model, phase transition