论文标题
对称随机哈密顿人的自由能亚辅助性
Free Energy Subadditivity for Symmetric Random Hamiltonians
论文作者
论文摘要
我们考虑一个随机的汉密尔顿$ h：σ\ to \ mathbb r $在紧凑型空间$σ$上定义的，该$σ$接纳了紧凑型组$ \ mathcal g $的传递动作。当$ h $的法律为$ \ MATHCAL G $ -INVARIANT时，我们显示其预期的自由能相对于$σ$ obeys of $ h $本身的独特$ \ Mathcal g $ invariant概率措施。对于弱小的疾病而言，这种界限通常是紧密的，并且在$ h $是高斯过程时会在不同温度下进行自由能。讨论了许多示例，包括分支随机步行，几个自旋眼镜，随机约束满意度问题以及随机场ISING模型。我们还向量子Hamiltonians提供了对量子SK和SYK模型的应用。
We consider a random Hamiltonian $H:Σ\to\mathbb R$ defined on a compact space $Σ$ that admits a transitive action by a compact group $\mathcal G$. When the law of $H$ is $\mathcal G$-invariant, we show its expected free energy relative to the unique $\mathcal G$-invariant probability measure on $Σ$ obeys a subadditivity property in the law of $H$ itself. The bound is often tight for weak disorder and relates free energies at different temperatures when $H$ is a Gaussian process. Many examples are discussed including branching random walk, several spin glasses, random constraint satisfaction problems, and the random field Ising model. We also provide a generalization to quantum Hamiltonians with applications to the quantum SK and SYK models.
