Disorder chaos in some diluted spin glass models
Disorder chaos in some diluted spin glass models
复制标题
一些稀释的自旋玻璃模型中的无序混乱
DOI：
10.1214/17-aap1331
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
D. Panchenko
中科院分区：
文献类型：
--
作者：
Wei;D. Panchenko
我们证明了三种具有大连通性参数的稀释模型在零温下的无序混沌：偶数$K\geq 2$的$K$-自旋反铁磁Ising模型，偶数$K\geq 2$的$K$-自旋玻璃模型，以及所有$K\geq 2$的随机$K$-sat模型.我们发现，修改即使是一小部分条款的结果在近极大化的原始和修改后的哈密顿量几乎是彼此正交的概率很高。我们使用一个标准的技术近似稀释模型适当的完全连接的模型，然后应用混乱的结果，在这种设置，其中包括以前已知的结果，以及新的例子激励随机$K$-SAT模型。
We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\geq 2$, $K$-spin spin glass model for even $K\geq 2$, and random $K$-sat model for all $K\geq 2$. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by appropriate fully connected models and then apply disorder chaos results in this setting, which include both previously known results as well as new examples motivated by the random $K$-sat model.