论文标题
用二次汉密尔顿的稀释自旋玻璃模型的自由能
Free energy of a diluted spin glass model with quadratic Hamiltonian
论文作者
论文摘要
我们研究了稀释的平均场自旋玻璃模型，该模型具有二次的哈密顿量。我们的主要结果是根据随机变量家族不可或缺的积分建立了限制自由能，这些变量是系统中旋转式旋转方差的弱极限，边缘连接变化。我们参数中的关键成分是通过识别这些随机变量作为递归分布方程的独特解决方案来启动的。我们的结果尤其提供了稀释的Shcherbina-Tirozzi模型的第一个示例，其限制自由能可以在任何反温度和外场中得出。
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our results in particular provide the first example of the diluted Shcherbina-Tirozzi model, whose limiting free energy can be derived at any inverse temperature and external field.
